Oliver Knill
Abstract
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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.
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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.
Key concepts: Pendulum, Elliptic function, Jacobi elliptic functions, Torus, Elliptic integral, Mathematics, Elliptic curve, Elliptic rational functions