Accession Number : AD0278275

Title :   UPPER AND LOWER BOUNDS FOR THE APSIDAL ANGLE IN THE THEORY OF THE SPHERICAL PENDULUM

Corporate Author : NAVAL ORDNANCE LAB WHITE OAK MD

Personal Author(s) : DIAZ,J.B. ; METCALF,F.T.

Report Date : JUN 1962

Pagination or Media Count : 21

Abstract : A simple method is developed for obtaining upper and lower bounds for the apsidal angle which occurs in the theory of the spherical pendulum. This method is employed to give a quick derivation of the well-known lower and upper bounds of Puiseux and Halphen (respectively) for the apsidal angle. The same method also yields readily the extension of Puiseux's lower bound discovered by W. Kohn. An advantage of the present method is the simplification which arises from eliminating the need for contour in egration. The sharpness of the bounds is also demonstrated. (Author)

Descriptors :   BODIES OF REVOLUTION, DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION, MOTION, SPHERES, THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE