Fourier analysis of the non-linear pendulum

Abstract

With developments in modern instrumentation such as microelectromechanical gyro/accelerometers, high speed video analysis, and precision shaft encoders, there is an increased interest in the study of the large angle oscillations of pendulums as an example of nonlinear dynamics. The solution to the equation of motion for the non-linear pendulum cannot be expressed in terms of elementary functions and is therefore generally approximated by a Fourier series. The present paper extends this to include Fourier coefficients up to A13, as required for amplitudes φ0≈π. The calculated coefficients are compared with experimental data for a damped and minimally damped pendulum for amplitudes φ0≈π.