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On the inverse variational problem in nonholonomic mechanics. (English) Zbl 1271.49027
Summary: The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constrained variationality is introduced on the basis of a recently discovered nonholonomic variational principle. Variational properties of first order mechanical systems with general nonholonomic constraints are studied. It is shown that constrained variationality is equivalent to the existence of a closed representative in the class of 2-forms determining the nonholonomic system. Together with the recently found constrained Helmholtz conditions this result completes basic geometric properties of constrained variational systems. A few examples of constrained variational systems are discussed.

MSC:
49N45 Inverse problems in optimal control
58E30 Variational principles in infinite-dimensional spaces
70F25 Nonholonomic systems related to the dynamics of a system of particles
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