Numerical integration of periodic orbits in the main problem of artificial satellite theory

DOI10.1007/BF00695787zbMath1446.70003MaRDI QIDQ2210912

Roger A. Broucke

Publication date: 9 November 2020

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Celestial mechanics (70F15) Orbital mechanics (70M20)

Related Items (13)

Bounded relative motion under zonal harmonics perturbations ⋮ Solution to the main problem of the artificial satellite by reverse normalization ⋮ Element sets for high-order Poincaré mapping of perturbed Keplerian motion ⋮ Exploring the long-term dynamics of perturbed Keplerian motion in high degree potential fields ⋮ Stability of the classical type of relative equilibria of a rigid body in the \(J_2\) problem ⋮ Contractivity-preserving explicit Hermite-Obrechkoff ODE solver of order 13 ⋮ Delaunay variables approach to the elimination of the perigee in artificial satellite theory ⋮ Hermite-Birkhoff-Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size ⋮ Bounded motion design in the Earth zonal problem using differential algebra based normal form methods ⋮ Bounded relative motions for formation flying in displaced orbits by low-thrust propulsion ⋮ An in-plane \(J_2\)-invariance condition and control algorithm for highly elliptical satellite formations ⋮ Bounded Martian satellite relative motion ⋮ Long-term passive distance-bounded relative motion in the presence of \(J_2\) perturbations

Cites Work

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• The possible motions of a satellite about an oblate planet
• The critical inclination in artificial satellite theory
• The critical inclination problem ? 30 years of progress
• The elimination of the parallax in satellite theory
• The problem of the critical inclination revisited
• Periodic and quasi-periodic Earth satellite orbits
• Reduction, Brouwer's Hamiltonian, and the critical inclination
• Canonical transformations depending on a small parameter
• The main problem of artificial satellite theory for small and moderate eccentricities
• The critical inclination problem with small eccentricity

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