Related papers: Relativistic forces in Lagangian mechanics
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…
An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this…
We present two types of relativistic Lagrangians for the Lorentz-Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends…
Forces parallel to particle trajectories occur in physically meaningful situations, including relativistic cosmology and Einstein frame scalar-tensor gravity. These situations have Newtonian analogues that we discuss to provide intuition…
There exist several approaches that investigate the connectedness of spacetime events through solutions of the Lorentz force equation. These approaches separate into three categories, that consider different equations. We clarify the…
Classical relativistic field theory is applied to perfect and magneto-hydrodynamic flows. The fields for Hamilton's principle are shown to be the Lagrangian coordinates of the fluid elements, which are potentials for the matter current…
We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of a slightly inhomogeneous intense laser field are obtained. In weak low-frequency background fields, such a particle on average…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the…
Modifications of General Relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein's theory by adding solely nondynamical fields. With the minimal…
It is proposed a Lagrangian for the quasi-rigid extended charged particle, which consists of a bare point particle term plus the standard electromagnetic minimal coupling. The quasi-rigid motion is imposed as a constraint. The extension of…
Relativistic hydrodynamics of an isentropic fluid in a gravitational field is considered as the particular example from the family of Lagrangian hydrodynamic-type systems which possess an infinite set of integrals of motion due to the…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in other terms. However, it seems that the Hamiltonian formalism…
It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz…
The Lagrangian relativistic direct interaction theory in the various forms of dynamics is formulated and its connections with the Fokker-type action theory and with the constrained Hamiltonian mechanics are established. The motion of…
Based on general considerations, the Standard Model of particle physics with its extensions (SM) can be ruled out as a valid theory of fundamental forces: it requires far too many parameters, which are not determined from first principles.…
We look over recent developments on our understanding about relativistic matter under external electromagnetic fields and mechanical rotation. I review various calculational approaches for concrete physics problems, putting my special…