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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…
In this paper, we handle the problem of the motion of the Foucault pendulum. We explore a new method induced from the De Alembert Principle giving the motional equations without small-amplitude oscillation approximation. The result of the…
When identifying instruments that have had great influence on the history of physics, none comes to mind more quickly than the pendulum. Though 'birthed' by Galileo in the 16th century, and in some respects nearly 'dead' by the middle of…
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors,…
This article aims to answer the question, "What is the simplest system that embodies the essence of Foucault's pendulum?" We study a very elementary idealized system that exhibits a precession behavior analogous to the classic pendulum. The…
In the course of basic physics, more precisely the course of classical mechanics should be understood as clearly as possible the subject of rotational dynamics for students of science and engineering, to have clarity with the issues…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the…
Using elementary geometric tools, we apply essentially the same methods to derive expressions for the rotation angle of the swing plane of Foucault's pendulum and the rotation angle of the spin of a relativistic particle moving in a…
We discuss a classical anisotropic oscillator and the Foucault pendulum as examples illustrating non-conservation of action variables in integrable classical mechanical systems with adiabatically slow evolution. We also emphasize the…
The change of the plane of oscillation of a Foucault pendulum is calculated without using equations of motion, the Gauss-Bonnet theorem, parallel transport, or assumptions that are difficult to explain.
We present an experimental setup to demonstrate normal modes and symmetry breaking in a two-dimensional pendulum. In our experiment we have used two modes of a single oscillator to demonstrate normal modes, as opposed to two single…
We present a pedagogical introduction to Floquet-Magnus theory through the classical example of Kapitza's pendulum - a simple system exhibiting nontrivial dynamical stabilization under rapid periodic driving. By deriving the equations of…
The purpose of this paper is to give an intuitive explanation of the Foucault pendulum precession (Fpp) by exploiting the easily proved result that infinitesimal spatial rotations about different axes in three dimensions are additive. This…
Stokes parameter formalism is applied to show the analogies between the motion of an asymmetric Foucault pendulum and several phenomena known from optics and atomic physics. Nonlinearity-induced precession of elliptical orbits of the…
The Atwood Machine, a classic apparatus in physics education, has historically been pivotal in demonstrating Newtonian mechanics, specifically Newton's Second Law. This study introduces an innovative adaptation, the circular Atwood machine,…
We have designed, built and operated a physical pendulum which allows one to demonstrate experimentally the behaviour of the pendulum under any equation of motion for such a device for any initial conditions. All parameters in the equation…
The main task of an introductory laboratory course is to foster students' manual, conceptual and statistical ability to investigate physical phenomena. Needing very simple apparatus, pendulum experiments are an ideal starting point in our…
A quantitative method is presented for stopping the intrinsic precession of a spherical pendulum due to ellipsoidal motion. Removing this unwanted precession renders the Foucault precession due to the turning of the Earth readily…
A treatment is given of the precession of a Foucault pendulum by means of two successive rotational transformations of coordinate system. The simplicity and accuracy of this approach is emphasized.