Open AccessComputing secular motion under slowly rotating quadratic perturbation
Author(s) -
Mikkola Seppo,
Nurmi Pasi
Publication year - 2006
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2006.10672.x
Subject(s) - physics , classical mechanics , angular momentum , perturbation (astronomy) , celestial mechanics , hamiltonian (control theory) , quadratic equation , equations of motion , two body problem , numerical integration , eccentricity (behavior) , secular variation , mathematical analysis , geometry , quantum mechanics , astronomy , mathematics , political science , law , mathematical optimization
We consider secular perturbations of nearly Keplerian two‐body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the secular Hamiltonian, we use angular momentum and eccentricity vectors as elements. The method of variation of constants then leads to a set of equations of motion that are simple and regular, thus allowing efficient numerical integration. Some possible applications are briefly described.