Gauge freedom in orbital mechanics

Annals of the New York Academy of Sciences

Volumn 1065, Issue , 2005, Pages 346-374

  Efroimsky, Michael ^a  

^a US NAVAL OBSERVATORY   (United States)

Author keywords

7Celestial mechanics; Gauge freedom; Orbital elements; Orbital mechanics; Osculating elements; Planetary equations

Indexed keywords

EID: 33751571563     PISSN: 00778923     EISSN: 17496632     Source Type: Book Series    
DOI: 10.1196/annals.1370.016     Document Type: Article

References (23)

1. EULER, L. 1748. Recherches sur la question des inegalites du mouvement de Saturne et de Jupiter, sujet propose pour le prix de l'annee. Berlin. Modern edition: L. Euler Opera mechanica et astronomica. Birkhauser-Verlag, Switzerland, 1999.
2. EULER, L. 1753. Theoria motus Lunae exhibens omnes ejus inaequalitates etc. Impensis Academiae Imperialis Scientarum Petropolitanae. St. Petersburg, Russia 1753. Modern edition: L. Euler Opera mechanica et astronomica. Birkhauser-Verlag, Switzerland 1999.
3. LAGRANGE, J.-L. 1778. Sur le Problμeme de la détermination des orbites des comètes d'après trois observations, 1-er et 2-ième mémoires. Nouveaux Mémoires de l'Académie de Berlin, 1778. Later edition: Euvres de Lagrange. Vol. IV, Gauthier-Villars, Paris 1869.
4. LAGRANGE, J.-L. 1783. Sur le Problμeme de la détermination des orbites des comètes d'après trois observations, 3-ième mémoire. Ibidem, 1783. Later edition: Áuvres de Lagrange. Vol. IV, Gauthier-Villars, Paris 1869.
5. LAGRANGE, J.-L. 1808. Sur la théorie des variations des éléments des planμetes et en particulier des variations des grands axes de leurs orbites. Lu, le 22 août 1808 à l'Institut de France. Later edition: Euvres de Lagrange.Vol.VI, pp.713-768, Gauthier-Villars, Paris 1877
6. LAGRANGE, J.-L. 1809. Sur la théorie générale de la variation des constantes arbitraires dans tous les problèmes de la mécanique. Lu, le 13 mars 1809 à l'Institut de France. Later edition: Evres de Lagrange.Vol.VI, 771-805, Gauthier-Villars, Paris 1877.
7. LAGRANGE, J.-L. 1810. Second mémoire sur la théorie générale de la variation des constantes arbitraires dans tous les problèmes de la mécanique". Lu, le 19 février 1810 à l'Institut de France. Later edition: Evres de Lagrange. Vol.VI, 809-816, Gauthier-Villars, Paris 1877.
8. NEWMAN, W. & M. EFROIMSKY. 2003. The method of variation of constants and multiple time scales in orbital mechanics. Chaos 13: 476-485.
9. GURFIL, P. & I. KLEIN. 2006. Mitigating the integration error in numerical simulations of Newtonian systems. Intl. J. Numerical Meth. Engin. Submitted.
10. EFROIMSKY, M. 2002. Equations for the orbital elements. Hidden symmetry. Preprint 1844, Institute of Mathematics and its Applications, University of Minnesota.
11. EFROIMSKY, M. 2002. The implicit gauge symmetry emerging in the N-body problem of celestial mechanics. astro-ph/0212245.
12. EFROIMSKY, M. & P. GOLDREICH. 2004. Gauge freedom in the N-body problem of celestial mechanics. Astron. Astrophys. 415: 1187-1199. astro-ph/0307130.
13. EFROIMSKY, M. & P. GOLDREICH. 2003. Gauge Symmetry of the N-body problem in the Hamilton-Jacobi approach. J. Math. Phys. 44: 5958-5977. astro-ph/0305344
14. EFROIMSKY, M. 2004. Long-term evolution of orbits about a precessing oblate planet. The case of uniform precession. astro-ph/0408168. (This preprint is a very extended version of the published paper Efroimsky Ref. 21. It contains all technical calculations omitted in the said publication.)
15. GOLDREICH, P. 1965. Inclination of satellite orbits about an oblate precessing planet. Astron. J. 70: 5-9.
16. BRUMBERG, V.A., L.S. EVDOKIMOVA & N.G. KOCHINA. 1971. Analytical methods for the orbits of artificial satellites of the Moon. Celest. Mech. 3: 197-221.
17. SLABINSKI, V. 2003. Satellite orbit plane perturbations using an Efroimsky gauge velocity. Talk at the 34th Meeting of the AAS Division on Dynamical Astronomy, Cornell University, May 2003.
18. 2-perturbed motion using mean non-osculating orbital elements. Celest. Mech. Dynam. Astron. 90: 289-306.
19. EFROIMSKY, M. 2005. Long-term evolution of orbits about a precessing oblate planet. 2. The case of variable precession. In preparation.
20. KINOSHITA, T. 1993. Motion of the orbital plane of a satellite due to a secular change of the obliquity of its mother planet. Celest. Mech. Dynam. Astron. 57: 359-368.
21. EFROIMSKY, M. 2005. Long-term evolution of orbits about a precessing oblate planet. 1. The case of uniform precession. Celest. Mech. Dynam. Astron. 91: 75-108.
22. LAINEY, V., P. GURFIL & M. EFROIMSKY. 2005. Long-term evolution of orbits about a precessing oblate planet. 3. A semianalytical and a purely numerical approaches. In preparation.
23. COLOMBO, G. 1966. Cassini's second and third laws. Astron. J. 71: 891-896.