NUMERICAL COMPUTATION OF INCOMPLETE ELLIPTIC INTEGRALS OF A GENERAL-FORM

We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combi nations of incomplete elliptic integrals of all kinds to a high precis ion. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when d ealing with many problems in celestial mechanics, including the analyt ic solution of the torque-free rotational motion of a rigid body aroun d its barycenter.