A time-dependent energy-momentum method

Abstract

We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisation of the relative equilibrium point notion to a non-autonomous realm is provided and studied. Relative equilibrium points of non-autonomous Hamiltonian systems are described via foliated Lie systems, which opens a new field of application of such differential equations. We reduce non-autonomous Hamiltonian systems via the Marsden-Weinstein theorem and we provide conditions ensuring the stability of the projection of relative equilibrium points to the reduced space. As an application, we study the stability of relative equilibrium points for a class of mechanical systems, which covers rigid bodies as a particular instance.

35 pages

Cited by in corpus (5)

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• Cosymplectic geometry, reductions, and energy-momentum methods with applications
• An energy-momentum method for ordinary differential equations with an underlying $k$-polysymplectic manifold
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• Reduction and reconstruction of multisymplectic Lie systems