Weierstrass elliptic functions for the pendulum
arXiv:2306.10653
Abstract
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the dynamics of the pendulum is translated linearly on the torus.
7 pages, 6 figures, in higher dimensions, we need initial conditions to commute