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arXiv · 1305.3974

Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems

M. Avendaño-Camacho·J. A. Vallejo·Yu. Vorobiev
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Abstract

We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with $\mathbb{S}^1 -$symmetry. Explicit global formulas for approximate second-order first integrals are derived. As examples, we analyze the case quadratic in the fast variables (in particular, the elastic pendulum), and the charged particle in a slowly-varying magnetic field.

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M. Avendaño-Camacho, J. A. Vallejo, Yu. Vorobiev. 2013-05-17. Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems. https://doi.org/10.1063/1.4817863

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