Numerical computation of incomplete elliptic integrals of a general form

Details Numerical computation of incomplete elliptic integrals of a general form Numerical computation of incomplete elliptic integrals of a general form

Jul 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..59..237f&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 59, no. 3, p. 237-251

Astronomy and Astrophysics

Astronomy

5

Algorithms, Elliptic Functions, Elliptical Orbits, Numerical Integration, Orbit Calculation, Center Of Gravity, Double Precision Arithmetic, Gravitational Fields, Rigid Structures, Rotation

Scientific paper

We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. 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 dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter.

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