Compatible Potentials and Orbits in Synodic Systems

Details Compatible Potentials and Orbits in Synodic Systems Compatible Potentials and Orbits in Synodic Systems

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..64..351b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 64, Issue 4, pp.351-361

Astronomy and Astrophysics

Astronomy

Inverse Problem

Scientific paper

For a given family of orbits f(x,y) = c * which can be traced by a material point of unit in an inertial frame it is known that all potentials V(x,y) giving rise to this family satisfy a homogeneous, linear in V(x,y), second order partial differential equation (Bozis,1984). The present paper offers an analogous equation in a synodic system Oxy, rotating with angular velocity ω. The new equation, which relates the synodic potential function Ω(x,y), = -V(x, y) + % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaaaa!3780![tfrac{1}{2}]ω2(x 2 + y 2) to the given family f(x,y) = c *, is again of the second order in Ω(x,y) but nonlinear. As an application, some simple compatible pairs of functions Ω(x,y) and f(x, y) are found, for appropriate values of ω, by adequately determining coefficients both in Ω and f.

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