Related papers: Relativistic forces in Lagangian mechanics
It is argued that there is a connection between the fundamental forces of electromagnetism and gravitation. This connection occurs because of: 1) the fundamental significance of the finite and invariant velocity of light in inertial…
In Continuum Mechanic a simple material body $\mathcal{B}$ is represeted by a three-dimensional differentiable manifold and the configuration space is given by the space of embeddings $Emb \left( \mathcal{B} , \mathbb{R}^{n} \right)$. We…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
It is proved that the class of stable interatomic potentials admits an exact representation in the form of a finite or infinite superposition of Yukawa potentials. An auxiliary scalar field is introduced to describe the dynamics of a system…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard…
We generalize previous work by considering a novel gravitational model with an action given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field and a kinetic term constructed from the gradients of the…
Equations of motions and energy-momentum density tensors are obtained for a dispersive and dissipative medium sustaining electric and magnetic polarizations, using Lagrangian formalisms. A previous work on the subject by the authors has…
Recent work by Philbin [1] has provided a Lagrangian theory that establishes a general method for the canonical quantization of the electromagnetic field in any dispersive, lossy, linear dielectric. Working from this theory, we extend the…
We propose a reformulation of gravitation in which the gravitational interaction is treated as a genuine force rather than an inertial effect arising from spacetime geometry. Within this framework, the difference between the affine…
We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed…
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and…
It is well known that magnetic force between two current carrying conductors is a relativistic manifestation of net electrostatic force between relatively moving electrons & protons of the two wires. On similar grounds but with more…
Relativistic rotation is considered in the limit of angular velocity approaching zero and radial distance approaching infinity, such that centrifugal acceleration is immeasurably small while tangent velocity remains close to the speed of…
This paper develops a general method to construct Ehrenfest-like relations for Lagrangian field theories when an external, coordinate-dependent scalar potential is applied. To do so, we derive continuity equations in which the spatial and…
The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for…
This paper contains results on geometric Routh reduction and it is a continuation of a previous paper where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction. In general, these reduced…
The relativistic energies and widths of hydrogen-like ions exposed to the uniform electric field are calculated. The calculations are performed for the ground and lowest excited states using the complex scaling technique in combination with…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…