A new discretization of the Kepler motion which conserves the Runge-Lenz vector

DOI10.1016/S0375-9601(02)00426-7zbMath1005.70009MaRDI QIDQ1852598

Yukitaka Minesaki, Yoshimasa Nakamura

Publication date: 6 January 2003

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

dynamical systemHamiltonian functionRunge-Lenz vectorKepler motionconstant-of-motion conservation

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Hamilton's equations (70H05) Two-body problems (70F05)

Related Items (13)

Adaptive symplectic conservative numerical methods for the Kepler problem ⋮ A one-parameter family of difference schemes for the numerical solution of the Keplerian problem ⋮ A new conservative numerical integration algorithm for the three-dimensional Kepler motion based on the Kustaanheimo-Stiefel regularization theory ⋮ О точности одного семейства адаптивных симплектических консервативных численных методов решения задачи Кеплера ⋮ On the conservativeness of a two-parameter family of three-stage symmetric-symplectic Runge-Kutta methods ⋮ Adaptive numerical methods for solving the problem about scattering on a force center ⋮ On stabilization of energy for Hamiltonian systems ⋮ A conservative discretization of the Kepler problem based on the \(L\)-transformations ⋮ An orbit-preserving discretization of the classical Kepler problem ⋮ Testing of adaptive symplectic conservative numerical methods for solving the Kepler problem ⋮ Parametrization of the solution of the Kepler problem and new adaptive numerical methods based on this parametrization ⋮ POST-STABILIZATION OF INVARIANTS AND APPLICATION TO NUMERICAL ANALYSIS OF CHAOS FOR SOME 3-DIMENSIONAL SYSTEMS ⋮ A super-integrable discretization of the Calogero model

Cites Work

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• Recent progress in the theory and application of symplectic integrators
• Discrete numerical methods in physics and engineering
• Non-existence of the modified first integral by symplectic integration methods. II: Kepler problem
• Multifold Kepler systems—Dynamical systems all of whose bounded trajectories are closed
• Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations

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