On the dynamics of nonholonomic systems
The authors begin with a discussion of whether or not the equations of motion in nonholonomic mechanics can be derived from a variational principle in the usual sense. This question correlates with the role of transpositional relations. Namely, in nonholonomic mechanics the special form of the principle of stationary action depends on the transpositional relations. The aim of this paper is the treatment of transpositional relations in their most general form (a new form of equations of motion for nonholonomic systems with linear or nonlinear constraints, and also for holonomic systems, will follow immediately). By using Hamilton's principle with nonzero transpositional relations, the authors deduce the so-called \(A\)-model. In the \(A\)-model, the dependent variations always lead to nonzero transpositional relations, whereas transpositional relations corresponding to independent variations can be nonzero. It is shown how the well-known equations of motion for holonomic and nonholonomic mechanics can be derived from the A-model. The results are illustrated on various nonholonomic Chaplygin systems: the generalized Voronets-Chaplygin system, the generalized Chaplygin system, the Routh-Chaplygin system, and the Gaponov-Chaplygin system.
scientific article; zbMATH DE number 5278422