A NEW FORMULATION OF THE 2-DIMENSIONAL INVERSE PROBLEM OF DYNAMICS

Taking the parameter b to vary along a monoparametric family of planar curves, given in the form x = x(lambda, b), y = y(lambda, b) (lambda being the parameter along each specific curve of the family), we deriv e two equations to formulate the inverse problem of dynamics and find all potentials creating, for adequate initial conditions, the given fa mily. One of these equations offers the total energy on each specific orbit traced under a known potential, the other equation relates merel y potentials and orbital data. This later equation lends itself to ser ies expansion solutions for small values of the parameter b. Two appli cations to isotach and geometrically similar orbits are discussed as s pecial cases and two examples are given to demonstrate the efficiency and the indispensability of the new equations.