Related papers: Symmetries of particle motion
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
We discuss the relativistic kinetic theory for a simple, collisionless, charged gas propagating on an arbitrary curved spacetime geometry. Our general relativistic treatment is formulated on the tangent bundle of the spacetime manifold and…
The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We are interested in the development of spherically symmetric geometries in $F(T)$ teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric…
In a coordinate free form are found the (deviation) equations satisfied by the (infinitesimal) deviation vector, relative velocity, relative momentum, relative acceleration and relative energy of two point particles in a differentiable…
We prove that autoparallel curves associated with a torsion-free but not necessarily metric-compatible affine connection can be derived from an action principle. We explicitly construct the action functional and show by standard variational…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…
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…
We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…
The parallel linear transports defined by flat linear connection are axiomatically described. On this basis a number of properties, some of which are new, of these transports and connections are derived.
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
In physics geometrical connections are the mean to create models with local symmetries (gauge connections), as well as general diffeomorphisms invariance (affine connections). Here we study the irreducible tensor decomposition of…
In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a horizontal plane. These papers addressed the…
The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths…
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…
The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter is discovered an exceptional class which is consistent with a vanishing affine connection. Based on…