Related papers: Third order variational equation for the free rela…
This note treats the notion of Lagrange derivative for the third order mechanics in the context of covariant Riemannian geometry. The variational differential equation for geodesic circles in two dimensions is obtained. The influence of the…
We consider open dynamical systems, subject to external interventions by agents that are not completely described by the theory (classical or quantal). These interventions are localized in regions that are relatively spacelike. Under these…
A third post-Newtonian (3 PN) equation of motion for two spherical compact stars in a harmonic coordinate has been derived based on the surface integral approach and the strong field point particle limit. The strong field point particle…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is…
The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and…
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…
We extend Noether's symmetry theorem to fractional action-like variational problems with higher-order derivatives.
The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that…
This work presents higher order Lagrangian dynamics possessing locally conformal character. More concretely, locally conformal higher order Euler-Lagrange equations are written with particular focus on the second- and the third-order cases.
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
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 consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion of a vortex filament with axial flow immersed in an…
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's…
Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of canonically conjugated…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
In Part I of this series, the author has shown how to extend the framework of Riemannian geometry so as to include infinitesimals of higher than first order. The purpose of the present contribution is to initiate an investigation into the…
Free vector fields, satisfying the Lorenz condition, are investigated in details in the momentum picture of motion in Lagrangian quantum field theory. The field equations are equivalently written in terms of creation and annihilation…
We consider stability of solitons of 3D Maxwell--Lorentz system with extended charged spinning particle.The solitons are solutions which correspond to a particle moving with a constant velocity $v\in\R^3$ with $|v|<1$ and rotating with a…
We define affine transport lifts on the tangent bundle by associating a transport rule for tangent vectors with a vector field on the base manifold. The aim is to develop tools for the study of kinetic/ dynamical symmetries in relativistic…