A symplectic integrator for Riemannian manifolds

DOI10.1007/BF02433475zbMath0862.70009OpenAlexW2023989006MaRDI QIDQ1924185

George W. Patrick, Benedict J. Leimkuhler

Publication date: 14 October 1996

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02433475

zbMATH Keywords

geodesic flowsparallel transport operatorsvelocity phase space

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items

Estimation of the Euler method error on a Riemannian manifold, B-stability of numerical integrators on Riemannian manifolds, Variational integrator based optimal feedback control for constrained mechanical systems, Mechanical integrators derived from a discrete variational principle, Energy-preserving methods on Riemannian manifolds, A Variational Approach to Multirate Integration for Constrained Systems

Cites Work

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• Numerical integration of ordinary differential equations on manifolds
• Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups
• Equivariant constrained symplectic integration
• Lie-Butcher theory for Runge-Kutta methods
• Symplectic Integration of Constrained Hamiltonian Systems
• Riemannian geometry