Non-integrability of the problem of motion around an oblate planet

DOI10.1007/BF00051896zbMath0827.70006OpenAlexW2009861230MaRDI QIDQ1894308

Alessandra Celletti, Piero Negrini

Publication date: 24 July 1995

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

Full work available at URL: https://doi.org/10.1007/bf00051896

zbMATH Keywords

phase spacechaotic motionsJ(2)-problemLerman theorem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Celestial mechanics (70F15)

Related Items (10)

First-order analytic propagation of satellites in the exponential atmosphere of an oblate planet ⋮ Analytical solutions for \(J_2\)-perturbed unbounded equatorial orbits ⋮ Solutions and periodicity of satellite relative motion under even zonal harmonics perturbations ⋮ Orbit determination with the two-body integrals. II ⋮ Solution to the main problem of the artificial satellite by reverse normalization ⋮ Preliminary orbits with line-of-sight correction for LEO satellites observed with radar ⋮ Delaunay variables approach to the elimination of the perigee in artificial satellite theory ⋮ Satellite onboard orbit propagation using Deprit's radial intermediary ⋮ Chaotic motion in axially symmetric potentials with oblate quadrupole deformation ⋮ On symplectic dynamics near a homoclinic orbit to 1-elliptic fixed point

Cites Work

• Unnamed Item
• Unnamed Item
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center
• Non integrability of the \(J_ 2\) problem
• On the motion of two-dimensional vortices with mass

This page was built for publication: Non-integrability of the problem of motion around an oblate planet