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- W4304697926 abstract "We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if and only if a certain 1-form is exact and a certain function vanishes (this function automatically vanishes for linear constraints). Moreover, this result can be extended to geodesic flows for arbitrary metric connections and the sufficient condition manifests as integrability of the torsion. As a consequence, volume-preservation of a nonholonomic system is closely related to the torsion of the nonholonomic connection. Examples of nonlinear/affine/linear constraints are considered." @default.
- W4304697926 created "2022-10-12" @default.
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- W4304697926 date "2020-09-23" @default.
- W4304697926 modified "2023-09-30" @default.
- W4304697926 title "Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints" @default.
- W4304697926 doi "https://doi.org/10.48550/arxiv.2009.11387" @default.
- W4304697926 hasPublicationYear "2020" @default.
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