zbMATH — the first resource for mathematics

Jet methods in nonholonomic mechanics. (English) Zbl 0758.70010
Summary: Classical nonholonomic mechanical systems are studied whose evolution space is a fiber bundle \(\tau: M\to\mathbb{R}\). The framework is that of jet spaces in which the geometrical meaning of the theory emerges clearly. For systems with linear constraints a new interpretation is given of Appell’s equations as first-order differential equations associated with a suitable vector field. The d’Alembert principle is formulated in an appropriate way to be generalized to systems with nonlinear constraints. The equivalence between the equations of motion arising from this generalization, the ones set up on Gauss’ principle of least constraint and Hertz’s principle of least curvature is established.

70F25 Nonholonomic systems related to the dynamics of a system of particles
55R10 Fiber bundles in algebraic topology
Full Text: DOI
[1] Hölder O., Nachr. 1896 pp 122– (1896)
[2] DOI: 10.1093/qjmam/7.3.338 · Zbl 0057.16002
[3] Vershik A. M., Sel. Math. Sov. 1 pp 339– (1981)
[4] Baryshnikov Yu. M., Uspekhi Mat. Nauk 45 pp 167– (1990)
[5] DOI: 10.1007/BF00282337 · Zbl 0606.58024
[6] Ehresmann C., C. R. Acad. Sci. 233 pp 598– (1951)
[7] Ehresmann C., Arch. Ration. Mech. Anal. 234 pp 1028– (1952)
[8] DOI: 10.5802/afst.593 · Zbl 0532.58001
[9] DOI: 10.5802/aif.120 · Zbl 0281.49026
[10] Appell P., C. R. Acad. Sci. Paris 129 pp 459– (1899)
[11] DOI: 10.1515/crll.1829.4.232 · ERAM 004.0157cj
[12] DOI: 10.1119/1.1976488
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.