http://mech.spbstu.ru/?title=Dynamics_of_a_particle_in_a_central_field&feed=atom&action=history Dynamics of a particle in a central field - Revision history 2024-03-29T12:49:26Z Revision history for this page on the wiki MediaWiki 1.27.3 http://mech.spbstu.ru/?title=Dynamics_of_a_particle_in_a_central_field&diff=8966&oldid=prev 188.243.39.146 at 15:41, 18 January 2017 2017-01-18T15:41:35Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:41, 18 January 2017</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[ru:Движение материальной точки в центральном поле]]</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Virtual laboratory]] &gt; [[Dynamics of a particle in a central field]] &lt;HR&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Virtual laboratory]] &gt; [[Dynamics of a particle in a central field]] &lt;HR&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[A.M. Krivtsov]]&lt;HR&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[A.M. Krivtsov]]&lt;HR&gt;</div></td></tr> <!-- diff cache key wikidb-mech_:diff:version:1.11a:oldid:7994:newid:8966 --> </table> 188.243.39.146 http://mech.spbstu.ru/?title=Dynamics_of_a_particle_in_a_central_field&diff=7994&oldid=prev Михаил Бабенков at 23:17, 8 June 2016 2016-06-08T23:17:22Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 23:17, 8 June 2016</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Virtual laboratory]] &gt; [[Dynamics of a particle in a central field]] &lt;HR&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Virtual laboratory]] &gt; [[Dynamics of a particle in a central field]] &lt;HR&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[<del class="diffchange diffchange-inline">А</del>.<del class="diffchange diffchange-inline">М</del>. <del class="diffchange diffchange-inline">Кривцов</del>]]&lt;HR&gt;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[<ins class="diffchange diffchange-inline">A</ins>.<ins class="diffchange diffchange-inline">M</ins>. <ins class="diffchange diffchange-inline">Krivtsov</ins>]]&lt;HR&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Interactive application, shown below, allows us to study <del class="diffchange diffchange-inline">the </del>trajectories of a particle in the central power-law potential field. Interaction force &lt;math&gt;F&lt;/math&gt; is a power function of distance &lt;math&gt;r&lt;/math&gt;:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Interactive application, shown below, allows us to study trajectories of a particle in the central power-law potential field. Interaction force &lt;math&gt;F&lt;/math&gt; is a power function of distance &lt;math&gt;r&lt;/math&gt;:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td> <td colspan="2" class="diff-lineno">Line 12:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:100%&quot; &gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:100%&quot; &gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''The text of the program is written in JavaScript:''' &lt;div class=&quot;mw-collapsible-content&quot;&gt; &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>'''The text of the program is written in JavaScript:''' &lt;div class=&quot;mw-collapsible-content&quot;&gt; &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Файл </del>'''&quot;FC.js&quot;'''</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">File</ins>'''&quot;FC.js&quot;'''</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;syntaxhighlight lang=&quot;javascript&quot; line start=&quot;1&quot; enclose=&quot;div&quot;&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;syntaxhighlight lang=&quot;javascript&quot; line start=&quot;1&quot; enclose=&quot;div&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>//The movement of a material point in the central field</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>//The movement of a material point in the central field</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>//A.M <del class="diffchange diffchange-inline">developer</del>. Krivtsov &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>//<ins class="diffchange diffchange-inline">developer </ins>A.M. Krivtsov &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>//18-21.05.2014 &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>//18-21.05.2014 &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>//Internet: tm.spbstu.ru/FC</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>//Internet: tm.spbstu.ru/FC</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l185" >Line 185:</td> <td colspan="2" class="diff-lineno">Line 185:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/syntaxhighlight&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/syntaxhighlight&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Файл </del>'''&quot;FC.html&quot;'''</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">File </ins>'''&quot;FC.html&quot;'''</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;syntaxhighlight lang=&quot;html5&quot; line start=&quot;1&quot; enclose=&quot;div&quot;&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;syntaxhighlight lang=&quot;html5&quot; line start=&quot;1&quot; enclose=&quot;div&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&#160;&#160; &#160; &lt;canvas id=&quot;canvasGraph&quot; width=&quot;600&quot; height=&quot;600&quot; style=&quot;border:1px solid #000000;&quot;&gt;&lt;/canvas&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&#160;&#160; &#160; &lt;canvas id=&quot;canvasGraph&quot; width=&quot;600&quot; height=&quot;600&quot; style=&quot;border:1px solid #000000;&quot;&gt;&lt;/canvas&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l243" >Line 243:</td> <td colspan="2" class="diff-lineno">Line 243:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The application allows to set the following parameters interactively: &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The application allows to set the following parameters interactively: &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;v_0&lt;/math&gt; is the initial velocity of the point. The initial velocity is directed perpendicular to the radial vector. Velocity is measured relatively to the &lt;math&gt;v_1&lt;/math&gt; <del class="diffchange diffchange-inline">is the circular speed </del>at the initial distance from the center (the first cosmic speed).&#160; &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;v_0&lt;/math&gt; is the initial velocity of the point. The initial velocity is directed perpendicular to the radial vector. Velocity is measured relatively to the <ins class="diffchange diffchange-inline">circular speed </ins>&lt;math&gt;v_1&lt;/math&gt; at the initial distance from the center (the first cosmic speed).&#160; &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;n&lt;/math&gt; is the index <del class="diffchange diffchange-inline">in </del>the law <del class="diffchange diffchange-inline">of interaction</del>(&lt;math&gt;n=-2&lt;/math&gt; corresponds to the gravitational interaction, &lt;math&gt;n=1&lt;/math&gt; is the <del class="diffchange diffchange-inline">linear-</del>elastic).&#160; &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;n&lt;/math&gt; is the index <ins class="diffchange diffchange-inline">of </ins>the <ins class="diffchange diffchange-inline">interaction </ins>law (&lt;math&gt;n=-2&lt;/math&gt; corresponds to the gravitational interaction, &lt;math&gt;n=1&lt;/math&gt; is the elastic <ins class="diffchange diffchange-inline">interaction</ins>).&#160; &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* zoom is the logarithmic scale (the logarithm to base 2). &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins class="diffchange diffchange-inline">&quot;</ins>zoom<ins class="diffchange diffchange-inline">&quot; </ins>is the logarithmic scale (the logarithm to base 2). &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;t_{\rm max}&lt;/math&gt; is the integration time expressed in terms of periods of circular motion &lt;math&gt;T&lt;/math&gt; at the initial distance from the center. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;t_{\rm max}&lt;/math&gt; is the integration time expressed in terms of periods of circular motion &lt;math&gt;T&lt;/math&gt; at the initial distance from the center. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l252" >Line 252:</td> <td colspan="2" class="diff-lineno">Line 252:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Research ideas ==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Research ideas ==</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* To find the possible trajectories &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* To find <ins class="diffchange diffchange-inline">all </ins>the possible trajectories &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* To define the dependence of the distance to the epicenter (the most distant point) of the orbit on &lt;math&gt;n&lt;/math&gt; and &lt;math&gt;u=v_0/v_1&lt;/math&gt;.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* To define the dependence of the distance to the epicenter (the most distant point) of the orbit on &lt;math&gt;n&lt;/math&gt; and &lt;math&gt;u=v_0/v_1&lt;/math&gt;.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* To find the closed trajectories of different topologies (for example, 5th, the 7th pointed stars, etc.) and to determine their position on the plane of &lt;math&gt;n&lt;/math&gt; and &lt;math&gt;u&lt;/math&gt; <del class="diffchange diffchange-inline">parameters</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* To find the closed trajectories of different topologies (for example, 5th, the 7th pointed stars, etc.) and to determine their position on the plane of <ins class="diffchange diffchange-inline">parameters </ins>&lt;math&gt;n&lt;/math&gt; and &lt;math&gt;u&lt;/math&gt;.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* To find a method for integrating the equations of motion with a variable step allowing to model the motion of a point at a large values of &lt;math&gt;|n|&lt;/math&gt; effectively.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* To find a method for integrating the equations of motion with a variable step allowing to model the motion of a point at a large values of &lt;math&gt;|n|&lt;/math&gt; effectively.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Fit the parameters values (and develop a handy method to do so), to obtain &quot;beautiful&quot; curves, which can be considered as Science Art objects (see in particular, last numbers of experiments). &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Fit the parameters values (and develop a handy method to do so), to obtain &quot;beautiful&quot; curves, which can be considered as Science Art objects (see in particular, <ins class="diffchange diffchange-inline">the </ins>last numbers of experiments). &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--[[Category: Virtual laboratory]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;!--[[Category: Virtual laboratory]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Programming]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Programming]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category: JavaScript]]--&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category: JavaScript]]--&gt;</div></td></tr> <!-- diff cache key wikidb-mech_:diff:version:1.11a:oldid:7843:newid:7994 --> </table> Михаил Бабенков http://mech.spbstu.ru/?title=Dynamics_of_a_particle_in_a_central_field&diff=7843&oldid=prev 192.168.0.2 at 12:18, 1 June 2016 2016-06-01T12:18:54Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 12:18, 1 June 2016</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6" >Line 6:</td> <td colspan="2" class="diff-lineno">Line 6:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>where &lt;math&gt;n&lt;/math&gt; is some real dimensionless <del class="diffchange diffchange-inline">degree </del>exponent. The attraction center is at <del class="diffchange diffchange-inline">the </del>&lt;math&gt;0&lt;/math&gt; point. &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>where &lt;math&gt;n&lt;/math&gt; is some real dimensionless exponent. The attraction center is at &lt;math&gt;0&lt;/math&gt; point. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;htmlet nocache=&quot;yes&quot;&gt;Krivtsov/FC_TM&lt;/htmlet&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;htmlet nocache=&quot;yes&quot;&gt;Krivtsov/FC_TM&lt;/htmlet&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l243" >Line 243:</td> <td colspan="2" class="diff-lineno">Line 243:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The application allows to set the following parameters interactively: &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The application allows to set the following parameters interactively: &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;v_0&lt;/math&gt; <del class="diffchange diffchange-inline">— </del>initial velocity of the point. The initial velocity is directed <del class="diffchange diffchange-inline">tangentially (</del>perpendicular to the radial <del class="diffchange diffchange-inline">direction)</del>.Velocity is measured <del class="diffchange diffchange-inline">in relation </del>to the &lt;math&gt;v_1&lt;/math&gt; <del class="diffchange diffchange-inline">- </del>speed <del class="diffchange diffchange-inline">circular motion on </del>the initial distance from the center (the first cosmic speed).&#160; &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;v_0&lt;/math&gt; <ins class="diffchange diffchange-inline">is the </ins>initial velocity of the point. The initial velocity is directed perpendicular to the radial <ins class="diffchange diffchange-inline">vector</ins>. Velocity is measured <ins class="diffchange diffchange-inline">relatively </ins>to the &lt;math&gt;v_1&lt;/math&gt; <ins class="diffchange diffchange-inline">is the circular </ins>speed <ins class="diffchange diffchange-inline">at </ins>the initial distance from the center (the first cosmic speed).&#160; &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;n&lt;/math&gt; <del class="diffchange diffchange-inline">— </del>is <del class="diffchange diffchange-inline">an </del>index in the law of interaction(&lt;math&gt;n=-2&lt;/math&gt; corresponds to the gravitational interaction, &lt;math&gt;n=1&lt;/math&gt; <del class="diffchange diffchange-inline">- </del>the linear-elastic).&#160; &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;n&lt;/math&gt; is <ins class="diffchange diffchange-inline">the </ins>index in the law of interaction(&lt;math&gt;n=-2&lt;/math&gt; corresponds to the gravitational interaction, &lt;math&gt;n=1&lt;/math&gt; <ins class="diffchange diffchange-inline">is </ins>the linear-elastic).&#160; &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* zoom is the logarithmic scale <del class="diffchange diffchange-inline">of display of the schedule </del>(the logarithm <del class="diffchange diffchange-inline">on the basis </del>2 <del class="diffchange diffchange-inline">is used</del>). &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* zoom is the logarithmic scale (the logarithm <ins class="diffchange diffchange-inline">to base </ins>2). &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;t_{\rm max}&lt;/math&gt; <del class="diffchange diffchange-inline">— </del>integration time expressed in &lt;math&gt;T&lt;/math&gt; <del class="diffchange diffchange-inline">periods of circular motion </del>at the initial distance from the center. &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* &lt;math&gt;t_{\rm max}&lt;/math&gt; <ins class="diffchange diffchange-inline">is the </ins>integration time expressed in <ins class="diffchange diffchange-inline">terms of periods of circular motion </ins>&lt;math&gt;T&lt;/math&gt; at the initial distance from the center. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Besides, it is possible to set &quot;number of the experiment&quot;. Every number has a separate set of four parameters named above and characterized by <del class="diffchange diffchange-inline">some </del>specific <del class="diffchange diffchange-inline">kind </del>of <del class="diffchange diffchange-inline">movement</del>. Experiments are ordered by &lt;math&gt;n&lt;/math&gt;(first), then by &lt;math&gt;v_0&lt;/math&gt;.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Besides <ins class="diffchange diffchange-inline">all</ins>, it is possible to set &quot;<ins class="diffchange diffchange-inline">a </ins>number of the experiment&quot;. Every number has a separate set of four parameters named above and characterized by <ins class="diffchange diffchange-inline">a </ins>specific <ins class="diffchange diffchange-inline">type </ins>of <ins class="diffchange diffchange-inline">motion</ins>.<ins class="diffchange diffchange-inline">&lt;!-- </ins>Experiments are ordered by &lt;math&gt;n&lt;/math&gt;(first), then by &lt;math&gt;v_0&lt;/math&gt;.<ins class="diffchange diffchange-inline">--&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== <del class="diffchange diffchange-inline">The proposed research areas </del>==</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== <ins class="diffchange diffchange-inline">Research ideas </ins>==</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* To <del class="diffchange diffchange-inline">define </del>possible <del class="diffchange diffchange-inline">variants of motion </del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* To <ins class="diffchange diffchange-inline">find the </ins>possible <ins class="diffchange diffchange-inline">trajectories </ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* To define the dependence of the distance to the epicenter (the most distant point) of the orbit <del class="diffchange diffchange-inline">from </del>&lt;math&gt;n&lt;/math&gt; and &lt;math&gt;u=v_0/v_1&lt;/math&gt;.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* To define the dependence of the distance to the epicenter (the most distant point) of the orbit <ins class="diffchange diffchange-inline">on </ins>&lt;math&gt;n&lt;/math&gt; and &lt;math&gt;u=v_0/v_1&lt;/math&gt;.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* To find closed trajectories of different topologies (for example, 5th, the 7th <del class="diffchange diffchange-inline">terminating </del>stars, etc.) and to determine their position on the plane of <del class="diffchange diffchange-inline">the parameters </del>&lt;math&gt;n&lt;/math&gt;<del class="diffchange diffchange-inline">, </del>&lt;math&gt;u&lt;/math&gt;.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* To find <ins class="diffchange diffchange-inline">the </ins>closed trajectories of different topologies (for example, 5th, the 7th <ins class="diffchange diffchange-inline">pointed </ins>stars, etc.) and to determine their position on the plane of &lt;math&gt;n&lt;/math&gt; <ins class="diffchange diffchange-inline">and </ins>&lt;math&gt;u&lt;/math&gt; <ins class="diffchange diffchange-inline">parameters</ins>.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* To find a method for integrating <del class="diffchange diffchange-inline">of </del>the equations of motion with a variable step allowing to model the <del class="diffchange diffchange-inline">movement </del>of a point at large &lt;math&gt;|n|&lt;/math&gt; effectively.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* To find a method for integrating the equations of motion with a variable step allowing to model the <ins class="diffchange diffchange-inline">motion </ins>of a point at <ins class="diffchange diffchange-inline">a </ins>large <ins class="diffchange diffchange-inline">values of </ins>&lt;math&gt;|n|&lt;/math&gt; effectively.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del class="diffchange diffchange-inline">• To pick up </del>values <del class="diffchange diffchange-inline">of parameters </del>(and <del class="diffchange diffchange-inline">to </del>develop a method <del class="diffchange diffchange-inline">of such selection</del>), <del class="diffchange diffchange-inline">allowing </del>to <del class="diffchange diffchange-inline">receive </del>&quot;beautiful&quot; <del class="diffchange diffchange-inline">schedules </del>which can be considered as <del class="diffchange diffchange-inline">objects of </del>Science Art (see in particular, last numbers of experiments). &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins class="diffchange diffchange-inline">Fit the parameters </ins>values (and develop a <ins class="diffchange diffchange-inline">handy </ins>method <ins class="diffchange diffchange-inline">to do so</ins>), to <ins class="diffchange diffchange-inline">obtain </ins>&quot;beautiful&quot; <ins class="diffchange diffchange-inline">curves, </ins>which can be considered as Science Art <ins class="diffchange diffchange-inline">objects </ins>(see in particular, last numbers of experiments). &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Virtual laboratory]]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;!--</ins>[[Category: Virtual laboratory]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Programming]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Programming]]</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category: JavaScript]]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Category: JavaScript]]<ins class="diffchange diffchange-inline">--&gt;</ins></div></td></tr> <!-- diff cache key wikidb-mech_:diff:version:1.11a:oldid:7840:newid:7843 --> </table> 192.168.0.2 http://mech.spbstu.ru/?title=Dynamics_of_a_particle_in_a_central_field&diff=7840&oldid=prev 192.168.0.2 at 11:44, 1 June 2016 2016-06-01T11:44:52Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 11:44, 1 June 2016</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2" >Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[А.М. Кривцов]]&lt;HR&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[А.М. Кривцов]]&lt;HR&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Interactive application, shown below, allows us to study the trajectories of a particle in the central power-law potential field. Interaction force &lt;math&gt;F&lt;/math&gt; is a <del class="diffchange diffchange-inline">polynomial </del>function of distance &lt;math&gt;r&lt;/math&gt;:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Interactive application, shown below, allows us to study the trajectories of a particle in the central power-law potential field. Interaction force &lt;math&gt;F&lt;/math&gt; is a <ins class="diffchange diffchange-inline">power </ins>function of distance &lt;math&gt;r&lt;/math&gt;:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td></tr> </table> 192.168.0.2 http://mech.spbstu.ru/?title=Dynamics_of_a_particle_in_a_central_field&diff=7839&oldid=prev 192.168.0.2 at 11:44, 1 June 2016 2016-06-01T11:44:02Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 11:44, 1 June 2016</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2" >Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[А.М. Кривцов]]&lt;HR&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Developer:&#160; [[А.М. Кривцов]]&lt;HR&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Interactive application, shown below, allows us to study the trajectories of a particle in the central power-law potential field. <del class="diffchange diffchange-inline">The interaction </del>force &lt;math&gt;F&lt;/math&gt; is a <del class="diffchange diffchange-inline">degree </del>function of distance &lt;math&gt;r&lt;/math&gt;:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Interactive application, shown below, allows us to study the trajectories of a particle in the central power-law potential field. <ins class="diffchange diffchange-inline">Interaction </ins>force &lt;math&gt;F&lt;/math&gt; is a <ins class="diffchange diffchange-inline">polynomial </ins>function of distance &lt;math&gt;r&lt;/math&gt;:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;F \sim r^n,&lt;/math&gt;</div></td></tr> <!-- diff cache key wikidb-mech_:diff:version:1.11a:oldid:7782:newid:7839 --> </table> 192.168.0.2 http://mech.spbstu.ru/?title=Dynamics_of_a_particle_in_a_central_field&diff=7782&oldid=prev 213.110.201.38: Created page with "Virtual laboratory > Dynamics of a particle in a central field <HR> Developer: А.М. Кривцов<HR> Interactive application, shown below, allows us to study..." 2016-05-30T16:14:51Z <p>Created page with &quot;<a href="/Virtual_laboratory" title="Virtual laboratory">Virtual laboratory</a> &gt; <a href="/Dynamics_of_a_particle_in_a_central_field" title="Dynamics of a particle in a central field">Dynamics of a particle in a central field</a> &lt;HR&gt; Developer: <a href="/%D0%90.%D0%9C._%D0%9A%D1%80%D0%B8%D0%B2%D1%86%D0%BE%D0%B2" class="mw-redirect" title="А.М. Кривцов">А.М. Кривцов</a>&lt;HR&gt; Interactive application, shown below, allows us to study...&quot;</p> <p><b>New page</b></p><div>[[Virtual laboratory]] &gt; [[Dynamics of a particle in a central field]] &lt;HR&gt;<br /> Developer: [[А.М. Кривцов]]&lt;HR&gt;<br /> <br /> Interactive application, shown below, allows us to study the trajectories of a particle in the central power-law potential field. The interaction force &lt;math&gt;F&lt;/math&gt; is a degree function of distance &lt;math&gt;r&lt;/math&gt;:<br /> <br /> :&lt;math&gt;F \sim r^n,&lt;/math&gt;<br /> <br /> where &lt;math&gt;n&lt;/math&gt; is some real dimensionless degree exponent. The attraction center is at the &lt;math&gt;0&lt;/math&gt; point. <br /> <br /> &lt;htmlet nocache=&quot;yes&quot;&gt;Krivtsov/FC_TM&lt;/htmlet&gt;<br /> <br /> &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:100%&quot; &gt;<br /> '''The text of the program is written in JavaScript:''' &lt;div class=&quot;mw-collapsible-content&quot;&gt; <br /> Файл '''&quot;FC.js&quot;'''<br /> &lt;syntaxhighlight lang=&quot;javascript&quot; line start=&quot;1&quot; enclose=&quot;div&quot;&gt;<br /> //The movement of a material point in the central field<br /> //A.M developer. Krivtsov <br /> //18-21.05.2014 <br /> //Internet: tm.spbstu.ru/FC<br /> <br /> function MainFC(canvas) {<br /> <br /> // main parameters<br /> <br /> const m = 1.; // weight<br /> const a = 1.; // radius<br /> const P = 1.; // gravitation force<br /> <br /> // Derivative dimensional parameters<br /> <br /> const T = 2 * Math.PI * Math.sqrt(m * a / P); // period of the movement on a circular orbit<br /> const v1 = Math.sqrt(P * a / m); // speed of the movement on a circular orbit (the 1st space)<br /> <br /> // Variables<br /> <br /> var n, v0, zoom, t_max, dt;<br /> <br /> // setting of sliders <br /> <br /> Slider_01.min = 1; Slider_01.max = 22; Slider_01.step = 0.1; // v0 / v1 - initial velocity<br /> Slider_02.max = 6; Slider_02.min = -Slider_02.max; Slider_02.step = 0.01; // n - degree indicator <br /> Slider_03.min = 0; Slider_03.max = 6; Slider_03.step = 0.01; // zoom <br /> Slider_04.min = 0; Slider_04.max = 100; Slider_04.step = 0.1; // t_max/T - time for calculation <br /> Slider_05.min = 1; Slider_05.max = set_exp(0); Slider_05.step = 1; // N_exp - experiment number<br /> <br /> Slider_05.focus();<br /> <br /> // values of variables<br /> <br /> dt = T / 200; // integration step<br /> set_exp(6); // variables are set for experiment 6<br /> <br /> // display<br /> <br /> draw();<br /> <br /> // the functions which are started at change of values of sliders and text fields<br /> <br /> this.set_01 = function(input) { v0 = Number(input) * v1; draw(); } <br /> this.set_02 = function(input) { n = Number(input); draw(); } <br /> this.set_03 = function(input) { zoom = Number(input); draw(); } <br /> this.set_04 = function(input) { t_max = Number(input) * T; draw(); } <br /> this.set_05 = function(input) { set_exp(input); draw(); } <br /> <br /> // display<br /> <br /> function draw() <br /> { <br /> // optimizing<br /> <br /> var n1 = (1 - n) / 2;<br /> var dt1 = -P / m * Math.pow(a, -n) * dt;<br /> <br /> // Area of creation of the schedule<br /> <br /> const X_max = canvas.width, Y_max = canvas.height;<br /> var x_max, y_max, sx, sy, X0, Y0;<br /> <br /> x_max = y_max = Math.pow(2, zoom) * a; // size of area of display<br /> x_min = y_min = -x_max; <br /> <br /> sx = sy = Y_max / (y_max - y_min); // scale on an axis y<br /> X0 = Y0 = Y_max + y_min * sy; // the provision 0 of an axis y in screen coordinates<br /> <br /> // Initialization of graphics<br /> <br /> var context = canvas.getContext(&quot;2d&quot;); // context - for drawing<br /> context.clearRect(0, 0, X_max, Y_max); // clear screen<br /> <br /> // horizontal axis<br /> context.strokeStyle = 'lightgrey';<br /> context.beginPath();<br /> context.moveTo(0, Y0); context.lineTo(X_max, Y0);<br /> context.moveTo(X0, 0); context.lineTo(X0, Y_max);<br /> context.moveTo(X0 + a * sx, Y0); context.arc(X0, Y0, a * sx, 0, 2 * Math.PI);<br /> context.stroke();<br /> <br /> // inscription<br /> context.fillStyle = 'black';<br /> context.font = &quot;italic 20px Times&quot;;<br /> context.fillText(&quot;0&quot;, X0 - 15, Y0 - 7);<br /> <br /> // schedule <br /> context.strokeStyle = 'black';<br /> context.beginPath();<br /> var vx = v0, vy = 0;<br /> var x = 0, y = a;<br /> context.moveTo(X0, Y0 - a * sy);<br /> for (var t = 0; t &lt; t_max; t += dt)<br /> {<br /> var r2 = x * x + y * y;<br /> var rn = Math.pow(r2, n1);<br /> vx += x / rn * dt1;<br /> vy += y / rn * dt1;<br /> x += vx * dt; <br /> y += vy * dt; <br /> var X = X0 + x * sx; <br /> var Y = Y0 - y * sy; <br /> context.lineTo(X, Y);<br /> }<br /> context.stroke(); <br /> }<br /> <br /> // Experiment choice<br /> <br /> function set_exp(N_exp)<br /> { <br /> var k = Number(N_exp);<br /> <br /> // degree indicator initial velocity zoom max number of steps<br /> <br /> if (!--k) { n = -3; v0 = 1.004 * v1; zoom = 2.98; t_max = 17.4 * T; } // spiral <br /> if (!--k) { n = -2.9; v0 = 1.023 * v1; zoom = 2.98; t_max = 67.6 * T; } <br /> if (!--k) { n = -2.87; v0 = 1.029 * v1; zoom = 2.57; t_max = 21.6 * T; } <br /> if (!--k) { n = -2.87; v0 = 1.03 * v1; zoom = 2.96; t_max = 94.4 * T; } <br /> if (!--k) { n = -2.5; v0 = 1.135 * v1; zoom = 2.98; t_max = 31.1 * T; } // 2<br /> <br /> if (!--k) { n = -2; v0 = 1.25 * v1; zoom = 2; t_max = 20 * T; } // ellipse<br /> if (!--k) { n = -1; v0 = 1.25 * v1; zoom = 1; t_max = 26 * T; }<br /> if (!--k) { n = -1; v0 = 1.36 * v1; zoom = 1.18; t_max = 10.8 * T; } // 10<br /> if (!--k) { n = -1; v0 = 1.63 * v1; zoom = 1.87; t_max = 25.3 * T; }<br /> if (!--k) { n = -1; v0 = 1.93 * v1; zoom = 2.8; t_max = 8 * T; } // 3 !<br /> if (!--k) { n = -1; v0 = 2.31 * v1; zoom = 3.92; t_max = 64.1 * T; } // 11<br /> if (!--k) { n = -1; v0 = 2.43 * v1; zoom = 4.29; t_max = 61.8 * T; } // 8<br /> if (!--k) { n = -1; v0 = 2.74 * v1; zoom = 5.5; t_max = 85.5 * T; } // 5<br /> <br /> if (!--k) { n = -0.74; v0 = 2.665 * v1; zoom = 3.81; t_max = 18.8 * T; } // 5 <br /> <br /> if (!--k) { n = 0; v0 = 1.66 * v1; zoom = 1.39; t_max = 5.1 * T; } // 7 <br /> if (!--k) { n = 0; v0 = 2.7 * v1; zoom = 2.34; t_max = 8.9 * T; } // 9 <br /> if (!--k) { n = 0; v0 = 3.46 * v1; zoom = 3.03; t_max = 13.3 * T; } // 11 <br /> <br /> if (!--k) { n = 1; v0 = 2 * v1; zoom = 1.3; t_max = 1 * T; } // 11 <br /> <br /> if (!--k) { n = 2; v0 = 2.39 * v1; zoom = 1.18; t_max = 4.0 * T; } // 11 <br /> <br /> if (!--k) { n = 3; v0 = 3.58 * v1; zoom = 1.28; t_max = 1.8 * T; } // 7 <br /> if (!--k) { n = 3; v0 = 6.97 * v1; zoom = 1.87; t_max = 1.7 * T; } // 9<br /> if (!--k) { n = 3; v0 = 11.28 * v1; zoom = 2.13; t_max = 1.6 * T; } // 11 <br /> if (!--k) { n = 3; v0 = 16.13 * v1; zoom = 2.50; t_max = 1.6 * T; } // 13 <br /> <br /> if (!--k) { n = 3.29; v0 = 1.3 * v1; zoom = 0.48; t_max = 1.8 * T; } // 13 <br /> <br /> if (!--k) { n = 4; v0 = 3.36 * v1; zoom = 1.12; t_max = 1.1 * T; } // 5 ! <br /> if (!--k) { n = 4; v0 = 6.08 * v1; zoom = 1.44; t_max = 1.9 * T; } // 12 <br /> if (!--k) { n = 4; v0 = 9.52 * v1; zoom = 1.66; t_max = 0.9 * T; } // 7 ! <br /> if (!--k) { n = 4; v0 = 18.45 * v1; zoom = 2.18; t_max = 0.728 * T; } // 9 <br /> <br /> if (!--k) { n = 5; v0 = 7.15 * v1; zoom = 1.55; t_max = 0.6 * T; } // 5 ! <br /> <br /> if (!--k) { n = 4; v0 = 3.304 * v1; zoom = 1.12; t_max = 36.4 * T; } // 5 ~~~<br /> if (!--k) { n = 4; v0 = 9.394 * v1; zoom = 1.66; t_max = 19.6 * T; } // 7 ~~~ <br /> <br /> if (N_exp)<br /> {<br /> Text_01.value = v0 / v1; Slider_01.value = Text_01.value; // initial velocity <br /> Text_02.value = n; Slider_02.value = Text_02.value; // degree indicator<br /> Text_03.value = zoom; Slider_03.value = Text_03.value; // zoom<br /> Text_04.value = t_max / T; Slider_04.value = Text_04.value; // time for calculation <br /> Text_05.value = N_exp; Slider_05.value = Text_05.value; // number of experiment<br /> }<br /> <br /> return -k; // Если N_exp = 0 returns total of experiments, in other cases returns 0<br /> }<br /> }<br /> &lt;/syntaxhighlight&gt;<br /> Файл '''&quot;FC.html&quot;'''<br /> &lt;syntaxhighlight lang=&quot;html5&quot; line start=&quot;1&quot; enclose=&quot;div&quot;&gt;<br /> &lt;canvas id=&quot;canvasGraph&quot; width=&quot;600&quot; height=&quot;600&quot; style=&quot;border:1px solid #000000;&quot;&gt;&lt;/canvas&gt;<br /> <br /> &lt;!--Installation of parameters of interaction (text fields and sliders)--&gt;<br /> &lt;div&gt;<br /> &lt;font face= &quot;Times New Roman&quot;&gt;&lt;I&gt;<br /> v&lt;/I&gt;&lt;SUB&gt;0&lt;/SUB&gt; = &lt;input id=&quot;Text_01&quot; style=&quot;width: 4.2ex;&quot; required pattern=&quot;[-+]?([0-9]*\.[0-9]+|[0-9]+)&quot; oninput=&quot;<br /> // if not the number is entered - the line won't pass validation on a pattern above, and checkValidity () will return false<br /> if (!this.checkValidity()) return;<br /> app.set_01(this.value);<br /> document.getElementById('Slider_01').value = this.value;<br /> &quot;&gt;&lt;I&gt; v&lt;/I&gt;&lt;SUB&gt;1&lt;/SUB&gt; <br /> &lt;input type=&quot;range&quot; id=&quot;Slider_01&quot; style=&quot;width: 100px;&quot; oninput=&quot;app.set_01(this.value); document.getElementById('Text_01').value = this.value;&quot;&gt;<br /> n = &lt;input id=&quot;Text_02&quot; style=&quot;width: 4.2ex;&quot; required pattern=&quot;[-+]?([0-9]*\.[0-9]+|[0-9]+)&quot; oninput=&quot;<br /> if (!this.checkValidity()) return;<br /> app.set_02(this.value);<br /> document.getElementById('Slider_02').value = this.value;<br /> &quot;&gt;<br /> &lt;input type=&quot;range&quot; id=&quot;Slider_02&quot; style=&quot;width: 100px;&quot; oninput=&quot;app.set_02(this.value); document.getElementById('Text_02').value = this.value;&quot;&gt;<br /> &lt;/font&gt;<br /> &lt;/div&gt;<br /> &lt;div&gt;<br /> &lt;font face= &quot;Times New Roman&quot;&gt;<br /> zoom = &lt;input id=&quot;Text_03&quot; style=&quot;width: 4.2ex;&quot; required pattern=&quot;[-+]?([0-9]*\.[0-9]+|[0-9]+)&quot; oninput=&quot;<br /> // if not the number is entered - the line won't pass validation on a pattern above, and checkValidity () will return false<br /> if (!this.checkValidity()) return;<br /> app.set_03(this.value);<br /> document.getElementById('Slider_03').value = this.value;<br /> &quot;&gt; <br /> &lt;input type=&quot;range&quot; id=&quot;Slider_03&quot; style=&quot;width: 100px;&quot; oninput=&quot;app.set_03(this.value); document.getElementById('Text_03').value = this.value;&quot;&gt;<br /> &lt;I&gt;t&lt;/I&gt;&lt;SUB&gt;max&lt;/SUB&gt; = &lt;input id=&quot;Text_04&quot; style=&quot;width: 4.2ex;&quot; required pattern=&quot;[-+]?([0-9]*\.[0-9]+|[0-9]+)&quot; oninput=&quot;<br /> if (!this.checkValidity()) return;<br /> app.set_04(this.value);<br /> document.getElementById('Slider_04').value = this.value;<br /> &quot;&gt;&lt;I&gt; T&lt;/I&gt;<br /> &lt;input type=&quot;range&quot; id=&quot;Slider_04&quot; style=&quot;width: 100px;&quot; oninput=&quot;app.set_04(this.value); document.getElementById('Text_04').value = this.value;&quot;&gt;<br /> &lt;/font&gt;<br /> &lt;/div&gt;<br /> &lt;div&gt;<br /> &lt;font face= &quot;Times New Roman&quot;&gt;<br /> Number of experiment &lt;input id=&quot;Text_05&quot; style=&quot;width: 4.2ex;&quot; required pattern=&quot;[-+]?([0-9]*\.[0-9]+|[0-9]+)&quot; oninput=&quot;<br /> // if not the number is entered - the line won't pass validation on a pattern above, and checkValidity () will return false<br /> if (!this.checkValidity()) return;<br /> app.set_05(this.value);<br /> document.getElementById('Slider_05').value = this.value;<br /> &quot;&gt; <br /> &lt;input type=&quot;range&quot; id=&quot;Slider_05&quot; style=&quot;width: 100px;&quot; oninput=&quot;app.set_05(this.value); document.getElementById('Text_05').value = this.value;&quot;&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;script type=&quot;text/javascript&quot;&gt;var app = new MainFC (<br /> document.getElementById('canvasGraph')<br /> );&lt;/script&gt;<br /> &lt;/syntaxhighlight&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> The application allows to set the following parameters interactively: <br /> * &lt;math&gt;v_0&lt;/math&gt; — initial velocity of the point. The initial velocity is directed tangentially (perpendicular to the radial direction).Velocity is measured in relation to the &lt;math&gt;v_1&lt;/math&gt; - speed circular motion on the initial distance from the center (the first cosmic speed). <br /> * &lt;math&gt;n&lt;/math&gt; — is an index in the law of interaction(&lt;math&gt;n=-2&lt;/math&gt; corresponds to the gravitational interaction, &lt;math&gt;n=1&lt;/math&gt; - the linear-elastic). <br /> * zoom is the logarithmic scale of display of the schedule (the logarithm on the basis 2 is used). <br /> * &lt;math&gt;t_{\rm max}&lt;/math&gt; — integration time expressed in &lt;math&gt;T&lt;/math&gt; periods of circular motion at the initial distance from the center. <br /> <br /> Besides, it is possible to set &quot;number of the experiment&quot;. Every number has a separate set of four parameters named above and characterized by some specific kind of movement. Experiments are ordered by &lt;math&gt;n&lt;/math&gt;(first), then by &lt;math&gt;v_0&lt;/math&gt;.<br /> <br /> == The proposed research areas ==<br /> <br /> * To define possible variants of motion <br /> * To define the dependence of the distance to the epicenter (the most distant point) of the orbit from &lt;math&gt;n&lt;/math&gt; and &lt;math&gt;u=v_0/v_1&lt;/math&gt;.<br /> * To find closed trajectories of different topologies (for example, 5th, the 7th terminating stars, etc.) and to determine their position on the plane of the parameters &lt;math&gt;n&lt;/math&gt;, &lt;math&gt;u&lt;/math&gt;.<br /> * To find a method for integrating of the equations of motion with a variable step allowing to model the movement of a point at large &lt;math&gt;|n|&lt;/math&gt; effectively.<br /> * • To pick up values of parameters (and to develop a method of such selection), allowing to receive &quot;beautiful&quot; schedules which can be considered as objects of Science Art (see in particular, last numbers of experiments). <br /> <br /> [[Category: Virtual laboratory]]<br /> [[Category: Programming]]<br /> [[Category: JavaScript]]</div> 213.110.201.38