Gauge freedom in orbital mechanics

Annals of the New York Academy of Sciences
Michael Efroimsky

Abstract

Both orbital and attitude dynamics employ the method of variation of parameters. In a non-perturbed setting, the coordinates (or the Euler angles) are expressed as functions of the time and six adjustable constants called elements. Under disturbance, each such expression becomes ansatz, the "constants" being endowed with time dependence. The perturbed velocity (linear or angular) consists of a partial time derivative and a convective term containing time derivatives of the "constants." It can be shown that this construction leaves one with a freedom to impose three arbitrary conditions on the "constants" and/or their derivatives. Out of convenience, the Lagrange constraint is often imposed. It nullifies the convective term and thereby guarantees that under perturbation the functional dependence of the velocity upon the time and "constants" stays the same as in the undisturbed case. "Constants" obeying this condition are called osculating elements. The "constants" chosen to be canonical, are called Delaunay elements, in the orbital case, or Andoyer elements, in the spin case. (Because some of the Andoyer elements are time dependent, even in the free-spin case, the role of "constants" is played by the initial values of these elem...Continue Reading

References

Jun 5, 2003·Chaos·William I Newman, Michael Efroimsky

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Citations

Jul 2, 2008·Medicine, Health Care, and Philosophy·Gerben Meynen, Jacco Verburgt

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