Weierstrass elliptic functions for the pendulum
Dynamical Systems
2023-06-23 v2 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2306.10653,
title = {Weierstrass elliptic functions for the pendulum},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:2306.10653},
year = {2023}
}
Comments
7 pages, 6 figures, in higher dimensions, we need initial conditions to commute