Preservation of adiabatic invariants for disturbed Hamiltonian systems under variational discretization

The perturbation to conformal invariance and the numerical algorithm of Hamiltonian systems with disturbed forces under variational discretization are studied in this paper. Based on the discrete difference variational principles, the discrete Hamiltonian equations (variational integrators) for dyna...

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Bibliographic Details
Published in:Acta mechanica 2020-02, Vol.231 (2), p.783-793
Main Authors: Xia, Li-Li, Bai, Long
Format: Article
Language:English
Subjects:
Adiabatic flow
Algorithms
Chaos theory
Classical and Continuum Physics
Control
Discretization
Dynamical Systems
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Entropy
Hamiltonian functions
Harmonic oscillators
Heat and Mass Transfer
Integrators
Invariance
Invariants
Mathematical analysis
Numerical analysis
Original Paper
Perturbation methods
Solid Mechanics
Theoretical and Applied Mechanics
Variational principles
Vibration
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Summary:The perturbation to conformal invariance and the numerical algorithm of Hamiltonian systems with disturbed forces under variational discretization are studied in this paper. Based on the discrete difference variational principles, the discrete Hamiltonian equations (variational integrators) for dynamical systems are obtained in the undisturbed and the disturbed cases, respectively. The determining equations of perturbation to conformal invariance are established for disturbed Hamiltonian systems. The exact invariants of Noether type led by conformal invariance for an undisturbed Hamiltonian system are derived. For disturbed discrete Hamiltonian systems, the condition of perturbation to conformal invariance leading to adiabatic invariants is proposed. Two examples are considered: a simple harmonic oscillator and the Kepler problem. The dynamical analysis is given by using the numerical results.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-019-02571-z