A third-order intermediate orbit for planetary theory

DOI10.1007/BF01230884zbMath0511.70013MaRDI QIDQ4749262

David L. Richardson

Publication date: 1982

Published in: Celestial Mechanics (Search for Journal in Brave)

zbMATH Keywords

quadratic convergenceplanetaryextended phase-spacePoincare variablesaccurate to third order in secular termsperturbation method based on Lie seriessatellite and lunar theoriestheory of third-order intermediate orbitzero-inclination and eccentricity singularities

Mathematics Subject Classification ID

Hamilton's equations (70H05) Celestial mechanics (70F15) Orbital mechanics (70M20) Elliptic functions and integrals (33E05) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (6)

General planetary theory in elliptic functions ⋮ Numerical computation of incomplete elliptic integrals of a general form ⋮ On the expansions of intermediate orbit for general planetary theory ⋮ First order planetary perturbations with elliptic functions ⋮ The construction of a fifth-order Jupiter-Saturn motion: Analytical theory. I: Outline ⋮ The problem of small divisors in planetary motion

Cites Work

• On the elimination of short-period terms in second-order general planetary theory investigated by Hori's method
• The Hamiltonian transformation in quadratic lie transforms
• An accelerated elimination technique for the solution of perturbed Hamiltonian systems
• An improved transformation-elimination technique for the solution of perturbed Hamiltonian systems
• A new solution to the Main Problem of Lunar Theory
• Canonical transformations depending on a small parameter
• Construction of a general planetary theory of the first order

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