Edwards's Solution of Pendulum Oscillation
Edwards's Solution of Pendulum Oscillation
The masterful derivation by Harold Edwards [1] finally brings the vision of Abel to the wider audience it deserves. In addition to its elegance, the article provides a constructive approach for improving computations along elliptic curves. The new and simple addition rules have been widely appreciated, although less so for the ingenious function introduced in [1, Section 15]. As with the much earlier Weierstrass function, the Edwards function determines time-dependent solutions for a range of interesting Hamiltonian systems [2]. This Demonstration shows three interrelated examples, including one that describes the oscillation of a plane pendulum. The Edwards function is truly an amazing and beautiful, doubly periodic, meromorphic function!
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