<h2>AAS 95-327</h2><h2>Integral Surfaces With Space-Time Coordinates In the Gravitational Field of a Rotating System</h2><h4> M. E. Hough, Textron Defense Systems, Wilmington, MA</h4><h2> Abstract </h2>A new integration theory is formulated for dynamical systems with two degrees of freedom, in the gravitational field of a rotating system.  Four 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 integral surfaces with space-time coordinates.  These surfaces represent two independent solutions of a second-order kinematic system to which the original fourth-order system has been reduced.  An integral curve may be represented as the locus of intersection points of the integral surfaces.  The new theory is the theoretical basis for a method of analytic continuation of periodic orbits of the circular restricted problem.<br><br>