相关论文: An Alternative Treatment of the Foucault Pendulum
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…
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 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.
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…
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…
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 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…
The Foucault pendulum is shown to be an example of motion on a pseudo-surface, and the consequences of that are explored. In particular, its first and second fundamental forms are obtained, as well as its Gaussian and mean curvatures and…
One of the many surprising results found in the mechanics of rotating systems is the stabilization of a particle in a rapidly rotating planar saddle potential. Besides the counterintuitive stabilization, an unexpected precessional motion is…
We present an analysis of the motion of a simple torsion pendulum and we describe how, with straightforward extensions to the usual basic dynamical model, we succeed in explaining some unexpected features we found in our data, like the…
We study the apsidal precession of a Physical Symmetrical Pendulum (Allais' precession) as a generalization of the precession corresponding to the Ideal Spherical Pendulum (Airy's Precession). Based on the Hamilton-Jacobi formalism and…
The paper proposes an alternative to the Foucault pendulum for detecting various movements of rotation of the Earth. Calculations suggest that if the duration of a "free" fall becomes longer the eastward deflection will be amplified in…
The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle…
The inverted pendulum is a mechanical system with a rapidly oscillating pivot point. Using techniques similar in spirit to the methodology of effective field theories, we derive an effective Lagrangian that allows for the systematic…
A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be…
Second part of a didactic sequence of activities on some topics of Astronomy, related mainly with the real shape of the Earth, the gravitational interactions between our planet and other celestial bodies, and the resulting movement of the…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…
In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top…