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Dynamics of a particle in a central field - Revision history
2024-03-29T12:49:26Z
Revision history for this page on the wiki
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188.243.39.146 at 15:41, 18 January 2017
2017-01-18T15:41:35Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:41, 18 January 2017</td>
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<tr><td class='diff-marker'> </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]] > [[Dynamics of a particle in a central field]] <HR></div></td><td class='diff-marker'> </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]] > [[Dynamics of a particle in a central field]] <HR></div></td></tr>
<tr><td class='diff-marker'> </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:  [[A.M. Krivtsov]]<HR></div></td><td class='diff-marker'> </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:  [[A.M. Krivtsov]]<HR></div></td></tr>
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Михаил Бабенков at 23:17, 8 June 2016
2016-06-08T23:17:22Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 23:17, 8 June 2016</td>
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<tr><td class='diff-marker'> </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]] > [[Dynamics of a particle in a central field]] <HR></div></td><td class='diff-marker'> </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]] > [[Dynamics of a particle in a central field]] <HR></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:  [[<del class="diffchange diffchange-inline">А</del>.<del class="diffchange diffchange-inline">М</del>. <del class="diffchange diffchange-inline">Кривцов</del>]]<HR></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:  [[<ins class="diffchange diffchange-inline">A</ins>.<ins class="diffchange diffchange-inline">M</ins>. <ins class="diffchange diffchange-inline">Krivtsov</ins>]]<HR></div></td></tr>
<tr><td class='diff-marker'> </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'> </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 <math>F</math> is a power function of distance <math>r</math>:</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 <math>F</math> is a power function of distance <math>r</math>:</div></td></tr>
<tr><td class='diff-marker'> </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'> </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="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>:<math>F \sim r^n,</math></div></td><td class='diff-marker'> </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>:<math>F \sim r^n,</math></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'> </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 class="mw-collapsible mw-collapsed" style="width:100%" ></div></td><td class='diff-marker'> </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 class="mw-collapsible mw-collapsed" style="width:100%" ></div></td></tr>
<tr><td class='diff-marker'> </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:''' <div class="mw-collapsible-content">  </div></td><td class='diff-marker'> </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:''' <div class="mw-collapsible-content">  </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>'''"FC.js"'''</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>'''"FC.js"'''</div></td></tr>
<tr><td class='diff-marker'> </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><syntaxhighlight lang="javascript" line start="1" enclose="div"></div></td><td class='diff-marker'> </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><syntaxhighlight lang="javascript" line start="1" enclose="div"></div></td></tr>
<tr><td class='diff-marker'> </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'> </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  </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  </div></td></tr>
<tr><td class='diff-marker'> </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  </div></td><td class='diff-marker'> </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  </div></td></tr>
<tr><td class='diff-marker'> </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'> </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'> </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'> </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'> </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></syntaxhighlight></div></td><td class='diff-marker'> </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></syntaxhighlight></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>'''"FC.html"'''</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>'''"FC.html"'''</div></td></tr>
<tr><td class='diff-marker'> </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><syntaxhighlight lang="html5" line start="1" enclose="div"></div></td><td class='diff-marker'> </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><syntaxhighlight lang="html5" line start="1" enclose="div"></div></td></tr>
<tr><td class='diff-marker'> </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>     <canvas id="canvasGraph" width="600" height="600" style="border:1px solid #000000;"></canvas></div></td><td class='diff-marker'> </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>     <canvas id="canvasGraph" width="600" height="600" style="border:1px solid #000000;"></canvas></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'> </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'> </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="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:  </div></td><td class='diff-marker'> </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:  </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>* <math>v_0</math> is the initial velocity of the point. The initial velocity is directed perpendicular to the radial vector. Velocity is measured relatively to the <math>v_1</math> <del class="diffchange diffchange-inline">is the circular speed </del>at the initial distance from the center (the first cosmic speed).   </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>* <math>v_0</math> 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><math>v_1</math> at the initial distance from the center (the first cosmic speed).   </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>* <math>n</math> is the index <del class="diffchange diffchange-inline">in </del>the law <del class="diffchange diffchange-inline">of interaction</del>(<math>n=-2</math> corresponds to the gravitational interaction, <math>n=1</math> is the <del class="diffchange diffchange-inline">linear-</del>elastic).   </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>* <math>n</math> is the index <ins class="diffchange diffchange-inline">of </ins>the <ins class="diffchange diffchange-inline">interaction </ins>law (<math>n=-2</math> corresponds to the gravitational interaction, <math>n=1</math> is the elastic <ins class="diffchange diffchange-inline">interaction</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>* zoom is the logarithmic scale (the logarithm to base 2).  </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">"</ins>zoom<ins class="diffchange diffchange-inline">" </ins>is the logarithmic scale (the logarithm to base 2).  </div></td></tr>
<tr><td class='diff-marker'> </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>* <math>t_{\rm max}</math> is the integration time expressed in terms of periods of circular motion <math>T</math> at the initial distance from the center.  </div></td><td class='diff-marker'> </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>* <math>t_{\rm max}</math> is the integration time expressed in terms of periods of circular motion <math>T</math> at the initial distance from the center.  </div></td></tr>
<tr><td class='diff-marker'> </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'> </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'> </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'> </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'> </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'> </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  </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  </div></td></tr>
<tr><td class='diff-marker'> </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 <math>n</math> and <math>u=v_0/v_1</math>.</div></td><td class='diff-marker'> </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 <math>n</math> and <math>u=v_0/v_1</math>.</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 <math>n</math> and <math>u</math> <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><math>n</math> and <math>u</math>.</div></td></tr>
<tr><td class='diff-marker'> </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 <math>|n|</math> effectively.</div></td><td class='diff-marker'> </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 <math>|n|</math> 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 "beautiful" curves, which can be considered as Science Art objects (see in particular, last numbers of experiments).  </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 "beautiful" curves, which can be considered as Science Art objects (see in particular, <ins class="diffchange diffchange-inline">the </ins>last numbers of experiments).  </div></td></tr>
<tr><td class='diff-marker'> </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'> </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="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: Virtual laboratory]]</div></td><td class='diff-marker'> </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: Virtual laboratory]]</div></td></tr>
<tr><td class='diff-marker'> </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'> </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="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]]--></div></td><td class='diff-marker'> </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]]--></div></td></tr>
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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
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<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>
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<tr><td class='diff-marker'> </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>:<math>F \sim r^n,</math></div></td><td class='diff-marker'> </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>:<math>F \sim r^n,</math></div></td></tr>
<tr><td class='diff-marker'> </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'> </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 <math>n</math> is some real dimensionless <del class="diffchange diffchange-inline">degree </del>exponent. The attraction center is at <del class="diffchange diffchange-inline">the </del><math>0</math> point.  </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 <math>n</math> is some real dimensionless exponent. The attraction center is at <math>0</math> point.  </div></td></tr>
<tr><td class='diff-marker'> </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'> </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="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><htmlet nocache="yes">Krivtsov/FC_TM</htmlet></div></td><td class='diff-marker'> </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><htmlet nocache="yes">Krivtsov/FC_TM</htmlet></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l243" >Line 243:</td>
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<tr><td class='diff-marker'> </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'> </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="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:  </div></td><td class='diff-marker'> </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:  </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>* <math>v_0</math> <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 <math>v_1</math> <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).   </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>* <math>v_0</math> <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 <math>v_1</math> <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).   </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>* <math>n</math> <del class="diffchange diffchange-inline">— </del>is <del class="diffchange diffchange-inline">an </del>index in the law of interaction(<math>n=-2</math> corresponds to the gravitational interaction, <math>n=1</math> <del class="diffchange diffchange-inline">- </del>the linear-elastic).   </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>* <math>n</math> is <ins class="diffchange diffchange-inline">the </ins>index in the law of interaction(<math>n=-2</math> corresponds to the gravitational interaction, <math>n=1</math> <ins class="diffchange diffchange-inline">is </ins>the linear-elastic).   </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>).  </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).  </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>* <math>t_{\rm max}</math> <del class="diffchange diffchange-inline">— </del>integration time expressed in <math>T</math> <del class="diffchange diffchange-inline">periods of circular motion </del>at the initial distance from the center.  </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>* <math>t_{\rm max}</math> <ins class="diffchange diffchange-inline">is the </ins>integration time expressed in <ins class="diffchange diffchange-inline">terms of periods of circular motion </ins><math>T</math> at the initial distance from the center.  </div></td></tr>
<tr><td class='diff-marker'> </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'> </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 "number of the experiment". 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 <math>n</math>(first), then by <math>v_0</math>.</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 "<ins class="diffchange diffchange-inline">a </ins>number of the experiment". 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"><!-- </ins>Experiments are ordered by <math>n</math>(first), then by <math>v_0</math>.<ins class="diffchange diffchange-inline">--></ins></div></td></tr>
<tr><td class='diff-marker'> </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'> </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'> </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'> </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><math>n</math> and <math>u=v_0/v_1</math>.</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><math>n</math> and <math>u=v_0/v_1</math>.</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><math>n</math><del class="diffchange diffchange-inline">, </del><math>u</math>.</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 <math>n</math> <ins class="diffchange diffchange-inline">and </ins><math>u</math> <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 <math>|n|</math> 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><math>|n|</math> 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>"beautiful" <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).  </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>"beautiful" <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).  </div></td></tr>
<tr><td class='diff-marker'> </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'> </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"><!--</ins>[[Category: Virtual laboratory]]</div></td></tr>
<tr><td class='diff-marker'> </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'> </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">--></ins></div></td></tr>
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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'> </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:  [[А.М. Кривцов]]<HR></div></td><td class='diff-marker'> </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:  [[А.М. Кривцов]]<HR></div></td></tr>
<tr><td class='diff-marker'> </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'> </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 <math>F</math> is a <del class="diffchange diffchange-inline">polynomial </del>function of distance <math>r</math>:</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 <math>F</math> is a <ins class="diffchange diffchange-inline">power </ins>function of distance <math>r</math>:</div></td></tr>
<tr><td class='diff-marker'> </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'> </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="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>:<math>F \sim r^n,</math></div></td><td class='diff-marker'> </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>:<math>F \sim r^n,</math></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'> </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:  [[А.М. Кривцов]]<HR></div></td><td class='diff-marker'> </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:  [[А.М. Кривцов]]<HR></div></td></tr>
<tr><td class='diff-marker'> </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'> </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 <math>F</math> is a <del class="diffchange diffchange-inline">degree </del>function of distance <math>r</math>:</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 <math>F</math> is a <ins class="diffchange diffchange-inline">polynomial </ins>function of distance <math>r</math>:</div></td></tr>
<tr><td class='diff-marker'> </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'> </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="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>:<math>F \sim r^n,</math></div></td><td class='diff-marker'> </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>:<math>F \sim r^n,</math></div></td></tr>
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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 "<a href="/Virtual_laboratory" title="Virtual laboratory">Virtual laboratory</a> > <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> <HR> 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><HR> Interactive application, shown below, allows us to study..."</p>
<p><b>New page</b></p><div>[[Virtual laboratory]] > [[Dynamics of a particle in a central field]] <HR><br />
Developer: [[А.М. Кривцов]]<HR><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 <math>F</math> is a degree function of distance <math>r</math>:<br />
<br />
:<math>F \sim r^n,</math><br />
<br />
where <math>n</math> is some real dimensionless degree exponent. The attraction center is at the <math>0</math> point. <br />
<br />
<htmlet nocache="yes">Krivtsov/FC_TM</htmlet><br />
<br />
<div class="mw-collapsible mw-collapsed" style="width:100%" ><br />
'''The text of the program is written in JavaScript:''' <div class="mw-collapsible-content"> <br />
Файл '''"FC.js"'''<br />
<syntaxhighlight lang="javascript" line start="1" enclose="div"><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("2d"); // 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 = "italic 20px Times";<br />
context.fillText("0", 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 < 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 />
</syntaxhighlight><br />
Файл '''"FC.html"'''<br />
<syntaxhighlight lang="html5" line start="1" enclose="div"><br />
<canvas id="canvasGraph" width="600" height="600" style="border:1px solid #000000;"></canvas><br />
<br />
<!--Installation of parameters of interaction (text fields and sliders)--><br />
<div><br />
<font face= "Times New Roman"><I><br />
v</I><SUB>0</SUB> = <input id="Text_01" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="<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 />
"><I> v</I><SUB>1</SUB> <br />
<input type="range" id="Slider_01" style="width: 100px;" oninput="app.set_01(this.value); document.getElementById('Text_01').value = this.value;"><br />
n = <input id="Text_02" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="<br />
if (!this.checkValidity()) return;<br />
app.set_02(this.value);<br />
document.getElementById('Slider_02').value = this.value;<br />
"><br />
<input type="range" id="Slider_02" style="width: 100px;" oninput="app.set_02(this.value); document.getElementById('Text_02').value = this.value;"><br />
</font><br />
</div><br />
<div><br />
<font face= "Times New Roman"><br />
zoom = <input id="Text_03" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="<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 />
"> <br />
<input type="range" id="Slider_03" style="width: 100px;" oninput="app.set_03(this.value); document.getElementById('Text_03').value = this.value;"><br />
<I>t</I><SUB>max</SUB> = <input id="Text_04" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="<br />
if (!this.checkValidity()) return;<br />
app.set_04(this.value);<br />
document.getElementById('Slider_04').value = this.value;<br />
"><I> T</I><br />
<input type="range" id="Slider_04" style="width: 100px;" oninput="app.set_04(this.value); document.getElementById('Text_04').value = this.value;"><br />
</font><br />
</div><br />
<div><br />
<font face= "Times New Roman"><br />
Number of experiment <input id="Text_05" style="width: 4.2ex;" required pattern="[-+]?([0-9]*\.[0-9]+|[0-9]+)" oninput="<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 />
"> <br />
<input type="range" id="Slider_05" style="width: 100px;" oninput="app.set_05(this.value); document.getElementById('Text_05').value = this.value;"><br />
</div><br />
<br />
<script type="text/javascript">var app = new MainFC (<br />
document.getElementById('canvasGraph')<br />
);</script><br />
</syntaxhighlight><br />
</div><br />
</div><br />
<br />
The application allows to set the following parameters interactively: <br />
* <math>v_0</math> — initial velocity of the point. The initial velocity is directed tangentially (perpendicular to the radial direction).Velocity is measured in relation to the <math>v_1</math> - speed circular motion on the initial distance from the center (the first cosmic speed). <br />
* <math>n</math> — is an index in the law of interaction(<math>n=-2</math> corresponds to the gravitational interaction, <math>n=1</math> - the linear-elastic). <br />
* zoom is the logarithmic scale of display of the schedule (the logarithm on the basis 2 is used). <br />
* <math>t_{\rm max}</math> — integration time expressed in <math>T</math> periods of circular motion at the initial distance from the center. <br />
<br />
Besides, it is possible to set "number of the experiment". Every number has a separate set of four parameters named above and characterized by some specific kind of movement. Experiments are ordered by <math>n</math>(first), then by <math>v_0</math>.<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 <math>n</math> and <math>u=v_0/v_1</math>.<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 <math>n</math>, <math>u</math>.<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 <math>|n|</math> effectively.<br />
* • To pick up values of parameters (and to develop a method of such selection), allowing to receive "beautiful" 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