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We study the precession of a Foucault pendulum using a new approach. We characterize the support anisotropy by the difference between the maximum and minimum periods of the pendulum along the principal axes of the support. Then we compute…

This paper investigates the spin precession of test particles moving in the equatorial plane of general stationary and axisymmetric spacetimes using the Mathisson-Papapetrou-Dixon equations. The spin precession angles for two cases, the…

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…

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…

The Fourier-based analysis customarily employed to analyze the dynamics of a simple pendulum is here revisited to propose an elementary iterative scheme aimed at generating a sequence of analytical approximants of the exact law of motion.…

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…

The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure…

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.

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…

In this paper we study the orbits of massive bodies moving in the spacetime generated by a spherically symmetric and non-rotating distribution of mass. More specifically, our treatment discusses the more accurate calculation of the…

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…

The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in…

Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…

We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney's problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half…

The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…

In the paper we consider systems in oscillating force fields such that the classical method of averaging can be applied. We present sufficient conditions for the existence of forced oscillations in such systems and study the asymptotic…

This paper considers a nonlinear spherical pendulum whose suspension point performs high-frequency spatial vibrations. The dynamics of this pendulum can be described by averaging its Hamiltonian over phases of vibrations. Rotationally…

This reading expounds with expediency on the recently proposed Azimuthally Symmetric Theory of Gravitation (ASTG) set-up earlier. At its inspection, it was demonstrated that the ASTG is capable (among others solar anomalies) of explaining…

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…

When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as…