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On the dynamics of systems with one-sided non-integrable constraints. (English) Zbl 1474.70018
Summary: In the paper we take the first steps in studying the dynamics of systems with one-sided differential constraints defined by inequalities in the phase space. We give a general definition of motion for systems with such constraints. Within the framework of the classical non-holonomic model, and also for systems with servoconstraints (according to Béghin), we present the conditions under which the system leaves two-sided differential constraints. As an example, we consider the Chaplygin sleigh with a one-sided constraint, which is realized by means of an anisotropic force of viscous friction. Variational principles for the determination of motion of systems with one-sided differential constraints are presented.
MSC:
70F25 Nonholonomic systems related to the dynamics of a system of particles
70H45 Constrained dynamics, Dirac’s theory of constraints
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