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• W2056557528 abstract "A mechanical system with perfect constraints can be described, under some mild assumptions, as a constrained Hamiltonian system(M, Ω, H, D, W): (M, Ω) (thephase space) is a symplectic manifold,H (theHamiltonian) a smooth function onM, D (theconstraint submanifold) a submanifold ofM, andW (theprojection bundle) a vector sub-bundle ofT D M, the reduced tangent bundle alongD. We prove that when these data satisfy some suitable conditions, the time evolution of the system is governed by a well defined differential equation onD. We define constrained Hamiltonian systems with symmetry, and prove a reduction theorem. Application of that theorem is illustrated on the example of a convex heavy body rolling without slipping on a horizontal plane. Two other simple examples show that constrained mechanical systems with symmetry may have an attractive (or repulsive) set of relative equilibria." @default.
• W2056557528 created "2016-06-24" @default.
• W2056557528 creator A5074584925 @default.
• W2056557528 date "1995-12-01" @default.
• W2056557528 modified "2023-09-26" @default.
• W2056557528 title "Reduction of constrained mechanical systems and stability of relative equilibria" @default.
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• W2056557528 doi "https://doi.org/10.1007/bf02099604" @default.
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