Abstract
The Lagrange equations of motion are written for a mechanical system consisting of kinematic dry-friction pairs. These equations are not solved for higher derivatives and constraint forces. The definition of a solution to them is given. Theorems on the uniqueness and existence of such a solution are formulated under certain sufficiently general additional assumptions. The results obtained develop and complement the mechanical theory of systems with dry friction [1‐6]. 1. The equations of motion are derived by the method of elimination of constraints, which is described in papers [7, 8]. According to this method, an initial system with constraints is changed for another system in which frictional constraints are replaced by reaction forces N 1 , …, and N m and friction forces. To describe the position of such a system, additional coordinates q n + 1 , …, q n + m are introduced along with the initial coordinates q 1 , …, q n . For the extended system under consideration, which is free of frictional constraints, an expression for kinetic energy T and the Lagrange equations of motion can be immediately determined. The kinetic energy T is assumed to be the quadratic form with respect to :
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