Statistics – Applications
Scientific paper
Feb 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002ima..rept....1e&link_type=abstract
Preprint No 1844 of the IMA (Institute of Applied Mathematics and its Applications), University of Minnesota
Statistics
Applications
12
Delaunay Elements, Delaunay Variables, Kepler Elements, Kepler Variables, Osculating Elements, Osculating Variables, Nonosculating Elements, Nonosculating Variables, Orbital Mechanics, Orbital Dynamics
Scientific paper
We revisit the Lagrange and Delaunay systems of equations of celestial mechanics, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This freedom of choice (=freedom of gauge fixing) reveals a symmetry hiding behind Lagrange's and Delaunay's systems, which is, mathematically, analogous to the gauge invariance in electrodynamics. Just like a convenient choice of gauge simplifies calculations in electrodynamics, so the freedom of choice of the submanifold may, potentially, be used to create simpler schemes of orbit integration. On the other hand, the presence of this feature may be a previously unrecognised source of numerical instability.
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