Related papers: Relativistic forces in Lagangian mechanics
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
Geometric formulation of Lagrangian relativistic mechanics in the terms of jets of one-dimensional submanifolds is generalized to Lagrangian theory of submanifolds of arbitrary dimension.
We study properties of classical reparametrization-invariant matter systems, mainly the relativistic particle and its d-brane generalization. The corresponding matter Lagrangian naturally contains background interaction fields, such as a…
We consider an extended theory of gravity with Lagrangian $\mathcal{L} = f(R,{\bf T}^{(n)})$, with ${\bf T}^{(n)}$ being a $2n$-th order invariant made of contractions of the energy-momentum tensor. When $n=1$ this theory reduces to…
We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
We derive the relativistic velocity addition law, the transformations of electromagnetic fields and space-time intervals by examining the drift velocities in a crossed electromagnetic field configuration. The postulate of the light velocity…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
In this work, we analyze a Lagrangian formalism recently proposed to approach the issue of the Abraham-Lorentz force. Instead of involving only position and velocity, as usual in Classical Mechanics, this Lagrangian involves the…
The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress-energy-momentum tensor for a hyperelastic body are derived from the gauge-invariant action…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
The Euler-Lagrange equations of motion for the most general Ricci type gravitational Lagrangians are derived by means of a purely metric formalism.
We recast Dirac's Lagrangian in quantum mechanics in the language of vector bundles and show that the action is an operator-valued connection one-form. Phases associated with change of frames of reference are seen to be total differentials…
The article determine a relativistic tensor of the second rank containing the vectors of the electric and magnetic polarization of the medium, based on the Maxwell equations and the determination of the charge density and polarization…
We argue that the definition of the thermodynamic work done on a charged particle by a time-dependent electromagnetic field is an open problem, because the particle's Hamiltonian is not gauge-invariant. The solution of this problem demands…
For a one-dimensional conservative systems with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the non relativistic case. With these functions, one shows the trajectories on the…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…