COMPATIBLE POTENTIALS AND ORBITS IN SYNODIC SYSTEMS

For a given family of orbits f(x, y) = c which can be traced by a mat erial point of unit in an inertial frame it is known that all potentia ls V(x, y) giving rise to this family satisfy a homogeneous, linear in V(x, y), second order partial differential equation (Bozis, 1984). Th e present paper offers an analogous equation in a synodic system Oxy, rotating with angular velocity omega. The new equation, which relates the synodic potential function Omega(x, y) = -V(x, y) + 1/2 omega(2)(x (2) + y(2)) to the given family f(x, y) = c, is again of the second o rder in Omega(x, y) but nonlinear. As an application, some simple comp atible pairs of functions Omega(x, y) and f(x, y) are found, for appro priate values of omega, by adequately determining coefficients both in Omega and f.