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Geometric mechanics on nonholonomic submanifolds. (English) Zbl 1248.70018
This paper aims to give a panorama on the title subject. A more explicative presentation is given in the introduction, that is enough clear and supported by the quoted references. Then the paper splits into three sections. 2. Mechanical systems in jet bundles (2.1 Basic structures; 2.2 Fibred mechanics). 3. Holonomic constraints. 4. Nonholonomic systems on constraint manifolds (4.1 Constraint submanifolds in jet bundles; 4.2 The canonical distribution; 4.3 Dynamics of nonholonomic systems: Reduced equations; 4.4 The non-holonomic variational principle; 4.5 Regularity and Hamilton equation of non-holonomic systems).
Reviewer’s remark. Let us emphasize that, as claimed by the author, this survey does not aim to be exhaustive, but it focuses only on particular aspects related to some topics studied by the same author and her co-workers (e.g., D. Krupka). With this respect, it may be suitable to underline that the actual state of the art of the subject considered in this paper strongly intersects the modern algebraic topology of PDE’s. In this sense this survey is really hold fashioned and few interesting.

MSC:
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70F25 Nonholonomic systems related to the dynamics of a system of particles
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