Gauge Freedom in Orbital Mechanics

Abstract

In orbital and attitude dynamics the coordinates and the Euler angles are expressed as functions of the time and six constants called elements. Under disturbance, the constants are endowed with time dependence. The Lagrange constraint is then imposed to guarantee that the functional dependence of the perturbed velocity on 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. (As some Andoyer elements are time dependent even in the free-spin case, the role of constants is played by their initial values.) The Andoyer and Delaunay sets of elements share a feature not readily apparent: in certain cases the standard equations render them non-osculating. In orbital mechanics, elements furnished by the standard planetary equations are non-osculating when perturbations depend on velocities. To preserve osculation, the equations must be amended with extra terms that are not parts of the disturbing function. In the case of Delaunay parameterisation, these terms destroy canonicity. So under velocity-dependent disturbances, osculation and canonicity are incompatible. (Efroimsky and Goldreich 2003, 2004) Similarly, the Andoyer elements turn out to be non-osculating under angular-velocity-dependent perturbation. Amendment of only the Hamiltonian makes the equations render nonosculating elements. To make them osculating, more terms must enter the equations (and the equations will no longer be canonical). In practical calculations, is often convenient to deliberately deviate from osculation by substituting the Lagrange constraint with a condition that gives birth to a family of nonosculating elements.

Talk at the annual Princeton conference ``New Trends in Astrodynamics" 2005 http://www.math.princeton.edu/astrocon/

Cited by in corpus (17)

• The Great Escape: How Exoplanets and Smaller Bodies Desert Dying Stars
• The orbital evolution of asteroids, pebbles and planets from giant branch stellar radiation and winds
• Sublimation-induced orbital perturbations of extrasolar active asteroids and comets: application to white dwarf systems
• A resonant-term-based model including a nascent disk, precession, and oblateness: application to GJ 876
• Constraining the Preferred-Frame ${\alpha }_1$, ${\alpha }_2$ parameters from Solar System planetary precessions
• The Serret-Andoyer Formalism in Rigid-Body Dynamics: I. Symmetries and Perturbations
• HEOSAT: A mean elements orbit propagator program for Highly Elliptical Orbits
• Long-term evolution of orbits about a precessing oblate planet. 2. The case of variable precession
• Planetary Orbital Equations in Externally-Perturbed Systems: Position and Velocity-Dependent Forces
• Long-term evolution of orbits about a precessing oblate planet. 3. A semianalytical and a purely numerical approach
• Analysis of the PPN Two-Body Problem Using Non-Osculating Orbital Elements
• A post-Newtonian gravitomagnetic effect on the orbital motion of a test particle around its primary induced by the spin of a distant third body
• Impact of mass transfer on the orbital evolution of a white dwarf close to an intermediate-mass black hole
• Gauge Theory for Finite-Dimensional Dynamical Systems
• Post-Keplerian perturbations of the hyperbolic motion in the field of a rotating massive object. Analysis in terms of osculating and nonosculating (contact) elements
• Tidal evolution of the Keplerian elements
• The dynamical evolution of close-in binary systems formed by a super-Earth and its host star. Case of the Kepler-21 system