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On The Power Series Solution to The Nonlinear Pendulum by W C Reinberger; M S Holland; N S Barlow; S J Weinstein is a Engineering article available to read on EtoBox.

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## Summary The exact solution to the simple pendulum problem has long been known in terms of Jacobi elliptic functions, of which an efficient numerical evaluation is standard in most scientific computing software packages. Alternatively, and as done in V. Fairén, López and L. Conde (Power series approximation to solutions of nonlinear systems of differential equation, Am. J. Phys. 56 (1988) 57–61], the pendulum equation can be analytically solved exactly by the power series solution method. Although recursive formulae for the series coefficients were provided in V. Fairén et al., the series itself—as well as the optimal location about which an expansion should be chosen to maximize the domain of convergence—has not yet been examined, and this is provided here. By virtue of its representation as an elliptic function, the pendulum function has singularities that lie off of the real axis in the complex time plane. This, in turn, imposes a radius of convergence on the power series solution in real time. By choosing the expansion point at the top of the trajectory, the power series converges all the way to the bottom of the trajectory without being affected by these singularities. We pr

Who reads On The Power Series Solution to The Nonlinear Pendulum?

Author

W C Reinberger; M S Holland; N S Barlow; S J Weinstein

Publisher

Oxford University Press (OUP)

Published

2022

Language

EN

Field

Engineering (Physical Sciences)