The Foucault Pendulum: Trajectories of the Full Lagrangian
Richard J. Mathar
Richard J. Mathar
Nov 2023
0被引用
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摘要原文
The Foucault Pendulum is a Spherical Pendulum of fixed length with two angular degrees of freedom, attached to a suspension which rotates once a day around the Earth axis at a distance essentially set by Earth radius and the geodetic latitude of the pendulum. We write the Lagrange Function in the inertial frame of the fixed Earth axis and couple it strictly to the rotating frame at which the suspension appears at rest. The Euler-Lagrange equations are a coupled system of second-order differential equations for the two coordinates of the mass projected on the local horizontal plane. These are solved numerically in a C++ program which allows to study the trajectories beyond the various standard approximations of the literature.
