Nonlinear spherical Foucault’s pendulum

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Abstract

The movement of a nonlinear spherical pendulum in the noninertial Earth’s system of reference is considered. The article consists of three parts.

The first part is devoted to the classical problem of the movement of the nonlinear spherical pendulum in inertial system of reference. We get some new results concerning the estimates of the apsidal angle. We give the critical analysis of previous publications (books and articles) on this problem.

The second one is devoted to the classical problem of the Foucault pendulum. We study the problem in nonlinear case and get some new results concerning the precession of the trajectory of the nonlinear pendulum with initial conditions that were used in Foucault pendulum’s experiment.

The third one (Application) is devoted to discussing and comparing this article’s results with previous results and explanations of the Foucault pendulum’ effects.

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About the authors

G. M. Rozenblat

Ishlinsky Institute for Problems in Mechanics RAS; Moscow State Automobile and Road Technical University (MADI)

Author for correspondence.
Email: gr51@mail.ru
Russian Federation, Moscow; Moscow

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Supplementary files

Supplementary Files
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2. Fig. 1. Spherical pendulum in the inertial coordinate system OXYZ

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3. Fig. 2. Incorrect trajectory of a spherical pendulum on a sphere (from the book by P. Appel [6, p. 435])

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4. Fig. 3. Correct trajectory of a spherical pendulum on a sphere (from the book by Synge and Griffiths [7, p. 377])

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