A new look at classical mechanics of constrained systems. (English) Zbl 0878.70009
Summary: A geometric formulation of classical analytical mechanics, especially suited to the study of nonholonomic systems, is proposed. The argument involves a preliminary study of the geometry of the space of kinetic states of the system, followed by a revision of Chetaev’s definition of virtual work, viewed here as a cornerstone for the implementation of the principle of determinism. Applications to ideal nonholonomic systems (equivalence between d’Alembert’s and Gauss’ principles, equations of motion) are explicitly worked out.
MSC:
| 70F25 | Nonholonomic systems related to the dynamics of a system of particles |
| 70H03 | Lagrange’s equations |
Keywords:
geometry of space of kinetic states; d’Alambert’s principle; Gauss’ principle; Chetaev’s definition of virtual work; principle of determinism; equations of motionReferences:
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