A primer on elliptic functions with applications in classical mechanics

Understand

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 problem of the planar pendulum, in fact, can be used to construct the general connection between the Jacobi and Weierstrass elliptic functions.
• The easy access to mathematical software by physics students suggests that they might reappear as useful tools in the undergraduate curriculum.