Solution of Lambert problem by reduction to rectilinear flight and study of the multiple solutions

A new approach to solving the Lambert problem of orbital mechanics is outlined. The principle of orbital isochronism is used to reduce the classical Lambert equations to simple and symmetrical forms for the cases of rectilinear flight. The family of solutions is studied with attention given to the nonuniqueness of the solution in the elliptical case when a multicircuit is allowed, and a set of criteria is established which allows the prediction of the solution paths before the problem is actually solved.