On the derivation of equations of motion in osculating elements

Authors

  • Tatiana N. Sannikova St.Petersburg State University, Universitetskaya nab., 7/9, St.Petersburg, 199034, Russian Federation;
  • Konstantin V. Kholshevnikov St.Petersburg State University, Universitetskaya nab., 7/9, St.Petersburg, 199034, Russian Federation; Institute of Applied Astronomy RAS, nab. Kutuzova, 10, St.Petersburg, 191187, Russian Fedration;
  • Mohammad S. Jazmati Qassim University, Buraidah, Kassim, Saudi Arabia

Abstract

It is shown that for deducing Euler type equations in a form that is invariant with respect to the rotation group SO(3) (for osculating elements: semi-major axis, eccentricity, mean anomaly) or with respect to the rotation group SO(2) (for inclination, longitude of ascending node, argument of pericentre) it is sufficient to use a representation via elements of the radius-vector r, but not of the velocity vector r˙. A method of deducing Euler type equations in projections on axes of coordinate systems commonly used in astronomy is pointed out. Refs 3.

Keywords:

osculating orbit, rotating reference frame, variation of osculating elements

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Published

2014-05-01

How to Cite

Sannikova, T. N., Kholshevnikov, K. V., & Jazmati, M. S. (2014). On the derivation of equations of motion in osculating elements. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 1(2), 340–344. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11060

Issue

Vol. 1 No. 2 (2014)

Section

Astronomy

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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