INTEGRAL SURFACES WITH SPACE-TIME COORDINATES, IN THE GRAVITATIONAL-FIELD OF A ROTATING SYSTEM

A new integration theory is formulated for dynamical systems with two degrees of freedom, in the gravitational field of a rotating system. F our integrals of motion may be determined from complete solutions of a system of three first-order, partial differential equations in three independent variables. The solutions of this system define two integra l surfaces with space-time coordinates. These surfaces represent two i ndependent solutions of a second-order kinematic system to which the o riginal fourth-order system has been reduced. An integral curve may be represented as the locus of intersection points of the integral surfa ces. The new theory is the theoretical basis for a method of analytic continuation of periodic orbits of the circular restricted problem.