A primer on elliptic functions with applications in classical mechanics

Abstract

The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the motion of a heavy symmetric top with one fixed point (Weierstrass). The planar pendulum can, in fact, be used to highlight an important connection between the Jacobi and Weierstrass elliptic functions. The easy access to mathematical software by physics students suggests that they might reappear as useful mathematical tools in the undergraduate curriculum.