Third-Order Solution to the Main Problem in Satellite Theory

DOI10.2514/3.56183zbMath0508.70010OpenAlexW2081782410MaRDI QIDQ4747621

André Deprit, Shannon L. Coffey

Publication date: 1982

Published in: Journal of Guidance, Control, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2514/3.56183

zbMATH Keywords

Poisson bracketseccentricitycritical inclinationartificial satellite theoryDelaunay variablesperigeecanonical Lie transformationelimination of parallaxanalytic third order solutionBrouwer's theorylong period termsparallax HamiltonianWhittaker's variables

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Astronomy and astrophysics (85A99) Celestial mechanics (70F15) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (20)

Frozen orbits for satellites close to an Earth-like planet ⋮ Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics ⋮ Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field ⋮ An analytical theory for the orbit of Nereid ⋮ Solution to the main problem of the artificial satellite by reverse normalization ⋮ Closed-form normalizations of perturbed two-body problems. ⋮ ATESAT: A symbolic processor for artificial satellite theory ⋮ Exploring the long-term dynamics of perturbed Keplerian motion in high degree potential fields ⋮ Mission design through averaging of perturbed Keplerian systems: the paradigm of an Enceladus orbiter ⋮ On the radial intermediaries and the time transformation in satellite theory ⋮ Delaunay variables approach to the elimination of the perigee in artificial satellite theory ⋮ Satellite onboard orbit propagation using Deprit's radial intermediary ⋮ A note on lower bounds for relative equilibria in the main problem of artificial satellite theory ⋮ Elimination of the perigee in the satellite problem ⋮ A new radial, natural, higher-order intermediary of the main problem four decades after the elimination of the parallax ⋮ Analytic orbit theory with any arbitrary spherical harmonic as the dominant perturbation ⋮ Decomposition of functions for elliptic orbits ⋮ Brouwer's satellite solution redux ⋮ Normal forms for perturbed Keplerian systems. ⋮ Complete zonal problem of the artificial satellite: generic compact analytic first order in closed form

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