**35th Meeting of the AAS Division on Dynamical Astronomy, April 2004**

*Session 8 Techniques*

Oral, Friday, April 23, 2004, 9:30am-12:55pm,
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## [8.03] The Physical Meaning and Application of Gauge Freedom in Orbital Mechanics

*W. I. Newman (University of California, Los Angeles), Michael Efroimsky (U. S. Naval Observatory, Washington)*

Gauge freedom emerges when the number of mathematical
variables exceeds the number of physical degrees of freedom
and, thus, generates a continuous group of
physically-equivalent reparametrisations of the theory. This
internal freedom may be interconnected with freedom of
coordinate-frame choice (e.g., general relativity) or may be
totally independent (e.g., electrodynamics and quantum
physics). Previously, we explained how gauge-type freedom
emerges in ordinary differential equations whenever the
variation-of-constants method is employed, and how this
freedom relates to multiple time scales. We illustrated this
by examples from linear and nonlinear dynamics.

In orbital mechanics gauge-type freedom emerges when we
relax the Lagrange constraint and, thus, model the perturbed
trajectory by a sequence of instantaneous Kepler ellipses
that are not tangent to the trajectory. It has been shown
that this approach is highly beneficial in problems related
to orbiting a precessing or non-precessing primary. Other
examples emerge in the motion of a body of a variable mass
as well as by orbital motion with relativistic effects

We provide an intuitive explanation for what gauge freedom
offers in terms of adapting to comoving frames. In celestial
mechanics there exists a subtle interplay between the
freedom of gauge and the freedom of frame choice, though
these freedoms are essentially of a different nature.

We provide a number of other examples of gauge-type freedom
being used to simplify practical calculations. These
examples range from stochastic problems to electromagnetism.
In particular, we focus upon gauge-type freedom emerging in
problems characterised by a separatrix and a homoclinic
point, and thereby have an unstable manifold. We show that
symplectic splitting methods also share gauge freedom. Since
a convenient gauge choice, combined with the choice of a
comoving frame, simplifies the underlying mathematics, this
freedom has the potential to simplify calculations in many
physical problems.

The author(s) of this abstract have provided an email address
for comments about the abstract:
win@ucla.edu

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Bulletin of the American Astronomical Society, **36** #2

© 2004. The American Astronomical Soceity.