Discrete Lagrange's equations and canonical equations based on the principle of least action

DOI10.1016/0096-3003(89)90100-8zbMath0672.70024OpenAlexW1992733731MaRDI QIDQ1120302

Toshiaki Itoh, Kanji Abe

Publication date: 1989

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(89)90100-8

zbMATH Keywords

Lie algebraharmonic oscillatordiscrete mechanicsdiscrete Poisson bracketsprinciple of least actioncontinuous mechanicsdifferentiation processesdiscrete canonical equationsdiscrete Liouville type theoremfinite difference quotients

Mathematics Subject Classification ID

Dynamics of a system of particles, including celestial mechanics (70F99) Hamiltonian and Lagrangian mechanics (70H99)

Related Items

An algebraic approach to discrete mechanics, Recent progress in the theory and application of symplectic integrators, Mechanical systems subject to holonomic constraints: Differential-algebraic formulations and conservative integration, Time integration and discrete Hamiltonian systems

Cites Work

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• First integrals in the discrete variational calculus
• On the energy theorem for the Lagrange equations in the discrete case
• Canonical transformation invariance and linear multistep formula for integration of Hamiltonian systems
• Hamiltonian differencing of fluid dynamics
• Hamiltonian-conserving discrete canonical equations based on variational difference quotients
• Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion. I: Motion of a single particle