Related papers: Third order variational equation for the free rela…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables…
We show that the Lorentz-Dirac equation is not an unavoidable consequence of energy-momentum conservation for a point charge. What follows solely from conservation laws is a less restrictive equation already obtained by Honig and Szamosi.…
We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.
In the present study, we analyze in combination the principles of special relativity and the phenomenon of the aberration of light, deriving a system of equations that allows establishing the relationship between the angles commonly…
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field…
The motion of three interacting point vortices in the plane can be thought of as the motion of three geometrical points endowed with a dynamics. This motion can therefore be re-formulated in terms of dynamically evolving geometric…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…
We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit…
Rigidity conditions for a body considered as a discrete system of relativistic particles are proposed. They by themselves do not yet determine an evolution of the system, and some second-order equations must be added to them.…
We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…
Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point,…
We study the problem of the motion of the free surface of a compressible fluid. We prove existence for the linearized equations.
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
A classical and a relativistic law of motion for an advancing shell are deduced applying the thin layer approximation. A new parameter connected with the quantity of absorbed matter in the expansion is introduced; this allows of matching…
In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top…
We study the problem of the motion of the free surface of a liquid. We prove existence and stability for the linearized equations.
We derive large-amplitude collective equations of motion from the variational principle for the time-dependent Schroedinger equation. These equations reduce to the well-known diabatic formulas for vibrational frequencies in the small…
A higher order theory of gravitation is considered which is obtained by modifying Einstein field equations. The Lagrange used to modify this in the form a polynomial in (scalar curvature) R. In this equation we have studied spherical…