Compatible potentials and orbits in synodic systems |
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| Authors: | George Bozis Magda Stavinschi |
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| Institution: | (1) Department of Theoretical Mechanics, University of Thessaloniki, GR-540 06 Thessaloniki, Greece;(2) Astronomical Institute of the Romanian Academy, RO-75212 Bucharest, Romania |
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| Abstract: | 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  . The new equation, which relates the synodic potential function  (x,y), = –V(x, y) + % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaaaa!3780!\\tfrac{1}{2}\]2(x
2 + y
2) to the given family f(x,y) = c
*, is again of the second order in (x,y) but nonlinear.As an application, some simple compatible pairs of functions (x,y) and f(x, y) are found, for appropriate values of , by adequately determining coefficients both in and f. |
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| Keywords: | Inverse problem |
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