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.
Keywords:
Lagrangian system, anisotropic friction, Painlevé condition
Citation:
Kozlov V. V., Lagrangian mechanics and dry friction, Rus. J. Nonlin. Dyn.,
2010, Vol. 6, No. 4,
pp. 855-868
DOI:10.20537/nd1004009