Difference between revisions of "Kelvin's medium"
From Department of Theoretical and Applied Mechanics
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| − | [[Виртуальная лаборатория]]>[[ | + | <!--[[Виртуальная лаборатория]]>[[One-dimensional Kelvin medium]] <HR>--> |
| − | Kelvin dimensional medium | + | Kelvin's one-dimensional medium is a chain consisting of solids interacting via a pair torque potential. In this example, the solids are visualized by rods. |
| − | The | + | The solids interact via the torque potential: |
::<math> | ::<math> | ||
U = C({\bf n}_{1}\cdot{\bf n}_{2}) | U = C({\bf n}_{1}\cdot{\bf n}_{2}) | ||
</math>, | </math>, | ||
| − | where C | + | where C is an interaction constant, n1, n2 are the unit vectors bound to the solids. The interaction torque is as follows: |
::<math> | ::<math> | ||
{\bf M}_{1} = {\bf n}_{1}\times\frac{\partial U}{\partial {\bf n}_{1}} = С({\bf n}_{1}\times{\bf n}_{2}) | {\bf M}_{1} = {\bf n}_{1}\times\frac{\partial U}{\partial {\bf n}_{1}} = С({\bf n}_{1}\times{\bf n}_{2}) | ||
Revision as of 03:43, 30 May 2016
Kelvin's one-dimensional medium is a chain consisting of solids interacting via a pair torque potential. In this example, the solids are visualized by rods.
The solids interact via the torque potential:
- ,
where C is an interaction constant, n1, n2 are the unit vectors bound to the solids. The interaction torque is as follows:
Then the motion equation of the k-th particle takes the form:
