相关论文: New vistas on the Laplace-Runge-Lenz vector

The characteristic feature of the Kepler Problem is the existence of the so-called Laplace--Runge--Lenz vector which enables a very simple discussion of the properties of the orbit for the problem. It is found that there are many classes of…

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…

It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular…

The main point of this paper is to examine a "hidden" dynamical symmetry connected with the conservation of Laplace-Runge-Lenz vector (LRL) in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM). The basic…

We study the Teleparallel Equivalent of General Relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether…

This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…

We develop a numerical scheme for the Kepler problem that preserves exactly all first integrals: angular momentum, total energy, and the Laplace-Runge-Lenz vector. This property ensures that orbital trajectories retain their precise shape…

We develop a general approach, based on the Lagrange-Noether machinery, to the definition of invariant conserved currents for gravity theories with general coordinate and local Lorentz symmetries. In this framework, every vector field \xi…

The Kepler problem in classical mechanics exhibits a rich structure of conserved quantities, highlighted by the Laplace--Runge--Lenz (LRL) vector. Through Noether's theorem in reverse, the LRL vector gives rise to a corresponding…

The universality of the Laplace-Runge-Lenz symmetry in all rotationally symmetric systems is discussed. The independence of the symmetry on the type of interaction is proven using only the most generic properties of the Poisson brackets.…

The equation for the conic sections describing the possible orbits in a potential $V \sim r^{-1}$ is obtained by means of a vector constant of the motion differing from the traditional Laplace-Runge-Lenz vector.

In Schwarzschild spacetime, the timelike geodesic equations, which define particle orbits, have a well-known formulation as a dynamical system in coordinates adapted to the timelike hypersurface containing the geodesic. For equatorial…

We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another…

Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…

We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…

Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They are a powerful tool to provide first integrals in classical mechanics and, in this respect, a new…

Conservation laws in gravitational theories with diffeomorphism and local Lorentz symmetry are studied. Main attention is paid to the construction of conserved currents and charges associated with an arbitrary vector field that generates a…

We first consider the Lagrangian formulation of general relativity for perturbations with respect to a background spacetime. We show that by combining Noether's method with Belinfante's "symmetrization'' procedure we obtain conserved…

A Noether-enhanced Legendre transformation from Lagrange densities to energy-momentum tensors is developed into an alternative framework for formulating classical field equations. This approach offers direct access to the Hamiltonian while…