Abstract
A review on the Foucault pendulum motion is presented using Cartesian coordinates for the ideal case and for small amplitude of oscillations. The choice of referential frames, the formulation and solution of Newton’s differential equation for the non-inertial frame of the Earth and the validity of the approximations used to simplify the determination of the solution are given. Using the angular position of the trajectory cusps, a new method to determine the precession angular velocity of the Foucault pendulum is shown. The pendulum bob trajectories and velocities for the referential frame in rotation with the Earth as well as for the inertial frame are given and the Chevilliet theorem was demonstrated. In addition, the pendulum bob trajectories are shown when an initial velocity is impinged in the direction perpendicular to the pendulum oscillation plane.
Highlights
In 1851 in the Pantheon in Paris, the French physicist Jean Bernard Leon Foucault made the public presentation of his pendulum [1]
The Foucault pendulum produced a great impact [2]; the experiment was repeated in many countries (USA and other European countries) and put to an end the philosophical discussions about Earth’s motion
Since 1851 much more than a hundred articles have addressed its use for didactic purposes in classical mechanics, various theoretical aspects on the pendulum motion as well as technical details of its construction
Summary
In 1851 in the Pantheon in Paris, the French physicist Jean Bernard Leon Foucault made the public presentation of his pendulum [1]. The exact solution of Newton’s differential equations in the threedimensional Cartesian coordinates is relatively elaborate to obtain [11] As it is well known and shown in this paper, very good approximations can be made to simplify the mathematical calculations. The purpose of this text is to present a review on the Foucault pendulum motion in the ideal case of small amplitudes of oscillation and without external interferences. This text is useful for students to follow many details on the motion of the Foucault pendulum in inertial and rotational frames and help in the study of the particle motion in frames performing rotation and translation
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