Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups
DOI10.3934/jgm.2023013zbMath1523.37070arXiv2202.00803OpenAlexW4321505813MaRDI QIDQ6160682
Álvaro Rodríguez Abella, Melvin Leok
Publication date: 26 June 2023
Published in: Journal of Geometric Mechanics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.00803
discrete mechanical systemsgeometric numerical integrationreduction by symmetriesLagrange-Poincaré-Dirac equations
Variational methods for problems in mechanics (70G75) Constrained dynamics, Dirac's theory of constraints (70H45) 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) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)
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