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 φ 0 ≈ π. The calculated coefficients are compared with experimental data for a damped and minimally damped pendulum for amplitudes φ 0 ≈ π.

中文翻译：

---

非线性摆的傅里叶分析

随着微机电陀螺仪/加速度计、高速视频分析和精密轴编码器等现代仪器的发展，人们对将摆的大角度振荡作为非线性动力学示例的研究越来越感兴趣。非线性摆的运动方程的解不能用初等函数表示，因此通常用傅立叶级数近似。本论文将其扩展为包括高达 A13 的傅立叶系数，这是振幅 φ 0 ≈ π 所需的。将计算出的系数与振幅 φ 0 ≈ π 的阻尼和最小阻尼摆的实验数据进行比较。