Other
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.1103g&link_type=abstract
American Astronomical Society, DDA meeting #40, #11.03; Bulletin of the American Astronomical Society, Vol. 41, p.904
Other
Scientific paper
The customary modeling of perturbed planetary and spacecraft motion as a continuous sequence of unperturbed two-body orbits (instantaneous ellipses) is conveniently assigned a physical interpretation through the Keplerian and Delaunay elements and complemented mathematically by the Lagrange-type equations which describe the evolution of these variables. If however the actual motion is very non-Keplerian (i.e. the perturbed orbit varies greatly from a two-body orbit), then its modeling by a sequence of conics is not necessarily optimal in terms of its mathematical description and its resulting physical interpretation.
Since, in principle a curve of any type can be represented as a sequence of points from a family of curves of any other type (Efroimsky 2005), alternate non-conic curves can be utilized to better describe the perturbed non-Keplerian motion of the body both mathematically and with a physically relevant interpretation. Non-Keplerian motion exists in both celestial mechanics and astrodynamics as evident by the complex interactions within star clusters and also as the result of a spacecraft accelerating via ion propulsion, solar sails and electro-dynamic tethers. For these cases, the sequence of simple orbits to describe the motion is not based on conics, but instead a family of spirals.
The selection of spirals as the underlying simple motion is supported by the fact that it is unnecessary to describe the motion in terms of instantaneous orbits tangent to the actual trajectory (Efroimsky 2002, Newman & Efroimsky 2003) and at times there is an advantage to deviate from osculation, in order to greatly simplify the resulting mathematics via gauge freedom (Efroimsky & Goldreich 2003, Slabinski 2003, Gurfil 2004).
From these two principles, (1) spirals as instantaneous orbits, and (2) controlled deviation from osculation, new planetary equations are derived for new non-osculating elements in the Frenet-Serret frame with the gauge function as a measure of non-osculation.
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