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On the simultaneous presence of unilateral and kinetic constraints in time-dependent impulsive mechanics. (English) Zbl 1112.70014

Summary: The simultaneous presence of unilateral and kinetic constraints acting on a mechanical system with a finite number of degrees of freedom is framed in the geometric context of left and right jet-bundles of the classical space-time bundle of the system. The survey gives three main cases and several subcases, some of which are mathematically correct but physically meaningless. The existence of at least one frame of reference for which the whole set of constraints can be at rest is the criterion selecting the physically relevant systems. For these systems, the conservation of kinetic energy, possibly together with a standard Gauss’s requirement on the impulsive reaction, is shown to give a well posed criterion of ideality of the constraints. The application of the criterion to several examples is presented and the corresponding results are critically analyzed.

MSC:

70F25 Nonholonomic systems related to the dynamics of a system of particles
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
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