改进E. Cartan关于非完整力学不变性的考虑

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2019-08-21 DOI:10.3934/JGM.2019022

W. M. Oliva, Gláucio Terra

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引用次数: 0

摘要

This paper concerns an intrinsic formulation of nonholonomic mechanics. Our point of departure is the paper [ 6 ], by Koiller et al., revisiting E. Cartan's address at the International Congress of Mathematics held in 1928 at Bologna, Italy ([ 3 ]). Two notions of equivalence for nonholonomic mechanical systems \begin{document}$ ( {\mathsf{{M}}}, {{\mathsf{{g}}}}, {\mathscr{D}}) $\end{document} are introduced and studied. According to [ 6 ], the notions of equivalence considered in this paper coincide. A counterexample is presented here showing that this coincidence is not always true.

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Improving E. Cartan considerations on the invariance of nonholonomic mechanics

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来源期刊

Journal of Geometric Mechanics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal: 1. Lagrangian and Hamiltonian mechanics 2. Symplectic and Poisson geometry and their applications to mechanics 3. Geometric and optimal control theory 4. Geometric and variational integration 5. Geometry of stochastic systems 6. Geometric methods in dynamical systems 7. Continuum mechanics 8. Classical field theory 9. Fluid mechanics 10. Infinite-dimensional dynamical systems 11. Quantum mechanics and quantum information theory 12. Applications in physics, technology, engineering and the biological sciences.