Difference between revisions of "Kelvin's medium"
From Department of Theoretical and Applied Mechanics
m (Михаил Бабенков moved page Kelvin medium to Kelvin's medium: shitty naming) |
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U = C({\bf n}_{1}\cdot{\bf n}_{2}) | U = C({\bf n}_{1}\cdot{\bf n}_{2}) | ||
</math>, | </math>, | ||
| − | where C is an interaction constant, | + | where <math>C</math> is an interaction constant, <math>\bf{n}_1</math>, <math>\bf{n}_2</math> 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 03:44, 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 is an interaction constant, , 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:
