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Skew-gradient representations of constrained mechanical systems. (English) Zbl 1322.70018

Summary: The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.

MSC:

70H45 Constrained dynamics, Dirac’s theory of constraints
70F20 Holonomic systems related to the dynamics of a system of particles
37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
37N05 Dynamical systems in classical and celestial mechanics
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