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

DOI10.1063/5.0071595OpenAlexW4306173660MaRDI QIDQ5883857

Meng-Meng Wu, Long Bai, Li-Li Xia

Publication date: 17 March 2023

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/5.0071595

Mathematics Subject Classification ID

Nonholonomic systems related to the dynamics of a system of particles (70F25) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Nonholonomic dynamical systems (37J60)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbation to symmetry and adiabatic invariants of discrete nonholonomic nonconservative mechanical system
• Hamel's formalism for infinite-dimensional mechanical systems
• Noether symmetries of discrete nonholonomic dynamical systems
• First integrals in the discrete variational calculus
• Integrators for nonholonomic mechanical systems
• Perturbation methods in group analysis
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Basic theory of fractional Mei symmetrical perturbation and its applications
• Conserved quantities of conservative continuous systems by Mei symmetries
• Relative controllability of fractional delay differential equations via delayed perturbation of Mittag-Leffler functions
• Preservation of adiabatic invariants for disturbed Hamiltonian systems under variational discretization
• Energy-preserving variational integrators for forced Lagrangian systems
• Two forms of the discrete equations and the Noether theorems for nonautonomous Birkhoffian systems
• Energy-preserving integrators applied to nonholonomic systems
• Perturbation to Noether symmetries and adiabatic invariants for disturbed Hamiltonian systems based on El-Nabulsi nonconservative dynamics model
• Nonholonomic mechanical systems with symmetry
• Mei symmetry of discrete mechanico-electrical systems
• A new type of conserved quantity induced by symmetries of Lagrange system
• Non-holonomic integrators
• Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems
• Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems
• Discrete mechanics and variational integrators
• Momentum and energy preserving integrators for nonholonomic dynamics
• Classical Dynamics
• Symplectic-energy-momentum preserving variational integrators
• Perturbation of Symmetries and Mei Adiabatic Invariants of Nonholonomic Systems with Servoconstraints
• Continuous symmetries of Lagrangians and exact solutions of discrete equations
• Parameterization Method for State-Dependent Delay Perturbation of an Ordinary Differential Equation
• New developments on the geometric nonholonomic integrator
• Quasivelocities and symmetries in non-holonomic systems
• Symmetries, Lagrangian Formalism and Integration of Second Order Ordinary Difference Equations
• Noether-type theorems for difference equations
• The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation