Rotation of the swing plane of Foucault's pendulum and Thomas spin precession: two sides of one coin

```@article{Krivoruchenko2008RotationOT,
title={Rotation of the swing plane of Foucault's pendulum and Thomas spin precession: two sides of one coin},
author={Mikhail I. Krivoruchenko},
journal={Physics-Uspekhi},
year={2008},
volume={52},
pages={821 - 829}
}```
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 circular orbit (the Thomas precession effect).
21 Citations
Foucault precession manifested in a simple system
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
On the difference between Wigner's and Møller's approaches to the description of Thomas precession
An account is given of the Wigner concept of particle spin and velocity rotations and of the variation of the angle between them under Lorentz transformations with noncollinear velocities. It is
Analysis on the Foucault pendulum by De Alembert Principle and Numerical Simulation
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
Electrodynamics in Uniformly Rotating Frames the Central Observer Point of View
In the current paper we present a generalization of the transforms of the electromagnetic field from the frame co-moving with a rotating observer aligned with the axis of rotation into an inertial
Electrodynamics in Uniformly Rotating Frames as Viewed from an Inertial Frame
AbstractIn the current paper we present a generalization of the transforms of the electromagnetic field from an inertial frame of reference into the frame co-moving with a uniformly rotating
Non-standard Lagrangians in rotational dynamics and the modified Navier–Stokes equation
We report some of the implications of non-standard Lagrangians in rotational dynamics. After deriving a new form of the Euler–Lagrange equation from the variational principle for the case of a
Permutation asymmetry of the relativistic velocity addition law and non-Euclidean geometry
The asymmetry of the relativistic addition law for noncollinear velocities under the velocity permutation leads to two modified triangles on a Euclidean plane depicting the addition of unpermuted and
On the question of the electromagnetic momentum of a charged body
The incorporation of a relativistic momentum of a nonelectromagnetic nature into macroscopic problems of electrodynamics obviates the lack of correspondence between the electromagnetic mass and the
A geometric invariant for the study of planar curves and its application to spiral tip meander
The use of the total curvature of the periodic arcs is demonstrated through a series of four examples from various branches of science to improve the modeling of spiral wave meander.
Exceptional and diabolical points in stability questions
“I never satisfy myself until I can make a mechanical model of a thing” – guided by this motto of Lord Kelvin we would like to invite a reader to look at some modern concepts such as a non‐Hermitian

References

SHOWING 1-10 OF 29 REFERENCES
A simple geometric model for visualizing the motion of a Foucault pendulum
• Physics
• 1987
A geometrical model of the Foucault pendulum is presented, which corrects some common misconceptions concerning the ‘‘fixed’’ plane in which the pendulum oscillates. It is shown visually, and by the
Foucault pendulum through basic geometry
• Physics, Education
• 2007
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how
Relativistic velocity space, Wigner rotation, and Thomas precession
• Physics
• 2004
We develop a relativistic velocity space called rapidity space from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive
The Motion of the Spinning Electron
IN a letter published in NATURE of February 20, p. 264, Messrs. Uhlenbeck and Goudsmit have shown how great difficulties which atomic theory had met in the attempt to explain spectral structure and
The Wigner angle as an anholonomy in rapidity space
A product of two non-collinear boosts (i.e., pure Lorentz transformations) can be written as the product of a boost and a rotation, the angle of rotation being known as Wigner’s angle. This paper
Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field
• Physics
• 1959
The problem of the precession of the “spin” of a particle moving in a homogeneous electromagnetic field — a problem which has recently acquired considerable experimental interest — has already been
The non-Euclidean style of Minkowskian relativity
The emergence and early history of a rival mathematical formalism to the Sommerfeld-Laue spacetime calculus for use in relativity theory is described.
Quantum mechanics: Non-relativistic theory,
• Physics
• 1958
The basic concepts of quantum mechanics Energy and momentum Schrodinger's equation Angular momentum Perturbation theory Spin The identity of particles The atom The theory of symmetry Polyatomic
On Unitary Representations of the Inhomogeneous Lorentz Group
It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally