Preservation of adiabatic invariants for disturbed Hamiltonian systems under variational discretization

Xia, Lili; Bai, Long

doi:10.1007/s00707-019-02571-z

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…For a given finite-difference equation (system), one can have the operators of the group admitted by the equation. Different types of difference equations which admit the different symmetry transformation operators can be obtained [10,11], and this theory is applied to search for discrete symmetries for dynamical systems [12,13]. Generally speaking, it needs to solve some linear partial finite-difference equations.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Xia

2021

Mathematics

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Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry preserving invariants are constructed based on the three points of the lattice and the characteristic equations. The difference scheme is constructed by using these discrete invariants. An example is presented to illustrate the applications of the results. The solutions of the invariant numerical schemes are compared to the noninvariant ones, the standard and the exact solutions.

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Section: Introductionmentioning

confidence: 99%

Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Xia

2021

Mathematics

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Preservation of adiabatic invariants and geometric numerical algorithm for disturbed nonholonomic systems

Xia

Bai

2022

Journal of Mathematical Physics

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Perturbations to Mei symmetry and the numerical algorithm of disturbed nonholonomic systems are studied under total variational discretization. The discrete equations on regular lattices of nonholonomic systems in the undisturbed and the disturbed cases are presented. The determining equations of Mei symmetry are established for undisturbed and disturbed systems. The exact invariants of Noether type led by Mei symmetry for undisturbed nonholonomic systems are given under infinitesimal transformations of Lie groups. For discrete disturbed nonholonomic systems, the condition of existence of adiabatic invariants led by perturbation to Mei symmetry and their forms are presented. The numerical simulations demonstrate that the geometric numerical algorithm has a higher precision and longer time stability than the standard numerical method.

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Preservation of adiabatic invariants for disturbed Hamiltonian systems under variational discretization

Cited by 2 publications

References 27 publications

Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Preservation of adiabatic invariants and geometric numerical algorithm for disturbed nonholonomic systems

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