Constrained normalization of Hamiltonian systems and perturbed Keplerian motion

DOI10.1007/BF00946760zbMath0606.70013MaRDI QIDQ1084886

Jan-Cees van der Meer

Publication date: 1986

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

Lunar problemconstrained Hamiltonian systemsartificial satellite theoryperturbed Kepler systemsstandard symplectic formsymplectic submanifoldnormalisation algorithm

Mathematics Subject Classification ID

Hamilton's equations (70H05) Two-body problems (70F05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Orbital mechanics (70M20)

Related Items

Reduced 4D oscillators and orbital elements in Keplerian systems: Cushman-Deprit coordinates, Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field, \((SO(3) \times \mathbb{T}^4)\)-reduction and relative equilibria for a radial axisymmetric intermediary model for roto-orbital motion, Bifurcations of the Hamiltonian fourfold 1:1 resonance with toroidal symmetry, Influence of planetary oblateness on Keplerian dynamics in magnetospheres and existence of invariant tori, Hamiltonian fourfold \(1:1\) resonance with two rotational symmetries, Normalization through invariants in \(n\)-dimensional Kepler problems, The constrained normal form algorithm, Normalization and the detection of integrability: The generalized van der Waals potential, Reduction and regularization of the Kepler problem, The Kepler system as a reduced 4D harmonic oscillator

Cites Work

• On the three-dimensional lunar problem and other perturbation problems of the Kepler problem
• The elimination of the parallax in satellite theory
• Regularization of kepler's problem and the averaging method on a manifold
• Nonlinear wave equations and constrained harmonic motion