2013/02/14 by Riccardo Borghi, Borghi, Riccardo
Computer Science · Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Computational Physics and Python Applications #Control and Stability of Dynamical Systems #Experimental and Theoretical Physics Studies #FOS: Physical sciences
paper · pdf · doi:10.48550/arxiv.1303.5023
openalex publication_date 2013/02/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Fourier-based analysis customarily employed to analyze the dynamics of a simple pendulum is here revisited to propose an elementary iterative scheme aimed at generating a sequence of analytical approximants of the exact law of motion. Each approximant is expressed by a Fourier sum whose coefficients are given by suitable linear combinations of Bessel functions, which are expected to be more accessible, especially at an undergraduate level, with respect to Jacobian elliptic functions. The first three approximants are explicitely obtained and compared with the exact solution for typical initial angular positions of the pendulum. In particular, it is shown that, at the lowest approximation level, the law of motion of the pendulum turns out to be adequately described, up to oscillation amplitudes of π/2, by a sinusoidal temporal behaviour with a frequency proportional to the square root of the so-called "besinc" function, well known in physical optics.