Lagrangian mechanics and dry friction
2010, Vol. 6, No. 4, pp. 855-868
Author(s): Kozlov V. V.
A generalization of Amantons’ law of dry friction for constrained Lagrangian systems is formulated. Under a change of generalized coordinates the components of the dry-friction force transform according to the covariant rule and the force itself satisfies the Painlevé condition. In particular, the pressure of the system on a constraint is independent of the anisotropic-friction tensor. Such an approach provides an insight into the Painlevé dry-friction paradoxes. As an example, the general formulas for the sliding friction force and torque and the rotation friction torque on a body contacting with a surface are obtained.
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