Difference between revisions of "Kelvin's medium"

Revision as of 20:19, 29 May 2016

Kelvin dimensional medium - chain consisting of a solids interacting via the torque capacities . In this example, solids visualized rods rigidly connected with the bodies themselves. The bodies interact by means of the torque capacities:

[math] U = C({\bf n}_{1}\cdot{\bf n}_{2}) [/math],

where C - constant characterizing the interaction, n1, n2 - the unit vector associated with the bodies. The moment of interaction:

[math] {\bf M}_{1} = {\bf n}_{1}\times\frac{\partial U}{\partial {\bf n}_{1}} = С({\bf n}_{1}\times{\bf n}_{2}) [/math]

Then the motion equation of the k-th particle takes the form:

[math] J\ddot{\bf \phi}_{k} = C(({\bf n}_{k}\times{\bf n}_{k+1}) + ({\bf n}_{k}\times{\bf n}_{k-1})) [/math]