The Non-forced Spherical Pendulum: Semi-numerical Solution

This manuscript deals with semi-numerical solutions of the equations of motion of the spherical pendulum. This pendulum has some azimuthal velocity and non-vanishing angular momentum. The cord restricts the motion to the surface of a sphere. We derive the system of coupled differential equations for the radial and azimuthal angles from the Lagrangian, solve them in terms of Elliptic Integrals, and provide a C++ program to print trajectories as a function of time utilizing the GNU scientific library. vixra:1909.0201