Transformations of the perturbed two-body problem to unperturbed harmonic oscillators

DOI10.1007/BF01231102zbMath0516.70013MaRDI QIDQ3664472

Victor R. Bond, Victor Szebehely

Publication date: 1983

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

zbMATH Keywords

Lyapunov-type stability of isoenergetic manifoldsperturbed planar problemradial variablesstability and transformationSundman's time variableunperturbed and undamped harmonic oscillators with constant coefficients

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Two-body problems (70F05) Orbital mechanics (70M20)

Related Items (16)

Sundman transformation and alternative tangent structures ⋮ A new set of integrals of motion to propagate the perturbed two-body problem ⋮ On the Szebehely-bond equation generalized Sundman's transformation for the perturbed two-body problem ⋮ Regularization and linearization of the equations of motion in central force-fields ⋮ Linearization in special cases of perturbed Keplerian motions ⋮ Infinitesimal time reparametrisation and its applications ⋮ Nonlocal Constants of Motions of Equations of Painlevé – Gambier Type and Generalized Sundman Transformation ⋮ On the radial intermediaries and the time transformation in satellite theory ⋮ The two-body global flow for negative energy under the Schwarzschild-de Sitter potential ⋮ A general canonical transformation increasing the number of variables with application to the two-body problem ⋮ Exact linearization of non-planar intermediary orbits in the satellite theory ⋮ Increased accuracy of computations in the main satellite problem through linearization methods ⋮ On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type ⋮ A transformation of the two-body problem ⋮ \(F\) and \(G\) Taylor series solutions to the Stark and Kepler problems with Sundman transformations ⋮ Nonlocal transformations of the generalized Liénard type equations and dissipative Ermakov-Milne-Pinney systems

Cites Work

• Unnamed Item
• Unnamed Item
• Canonical orbital elements in terms of an arbitrary independent variable
• The intermediate anomaly
• ON MOULTON'S ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES

This page was built for publication: Transformations of the perturbed two-body problem to unperturbed harmonic oscillators