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- W2028363048 abstract "We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained Hamiltonian system, which comprises the non-holonomic mechanical system as a dynamical subsystem on an invariant manifold. The embedding system possesses a completely natural structure in the context of symplectic geometry, and using it in order to understand properties of the subsystem has compelling advantages. We discuss generic geometric and topological properties of the critical sets of both embedding and physical system, using Conley-Zehnder theory and by relating the Morse-Witten complexes of the 'free' and constrained system to one another. Furthermore, we give a qualitative discussion of the stability of motion in the vicinity of the critical set. We point out key relations to sub-Riemannian geometry, and a potential computational application." @default.
- W2028363048 created "2016-06-24" @default.
- W2028363048 creator A5000267802 @default.
- W2028363048 date "2004-03-01" @default.
- W2028363048 modified "2023-09-27" @default.
- W2028363048 title "Critical manifolds and stability in Hamiltonian systems with non-holonomic constraints" @default.
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- W2028363048 doi "https://doi.org/10.1016/j.geomphys.2003.08.004" @default.
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