Related papers: Relativistic motion under constant force: velocity…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…
We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented,…
We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The…
We study the behavior in the remote past and future of solutions of an equation of motion for charged particles proposed by F. Rohrlich, for the special case in which the motion is in one spatial dimension. We show that if an external force…
Models of relativistic particle with Lagrangian ${\cal L}(k_1)$, depending on the curvature of the worldline $k_1$, are considered. By making use of the Frenet basis, the equations of motion are reformulated in terms of the principal…
When particle speeds are large the motion of a collisionless plasma is modeled by the relativistic Vlasov Maxwell system. Large time behavior of solutions which depend on one position variable and two momentum variables is considered. In…
We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a…
We study a general relativistic particle action obtained by incorporating the Hamiltonian constraints into the formalism as a toy model for general relativity and string theory. We show how a non-vanishing cosmological constant and a…
The theoretical foundation of the object moving faster than light in vacuum ({\it tachyon}) is still missing or incomplete. Here we present the classical foundation of the relativistic dynamics including the tachyon. An anomalous…
We have defined slowness (or reciprocal velocity) corresponding to v as cc/v, where c is the speed of light and v is the corresponding velocity. Velocity and slowness are images of each other. Reciprocal symmetric law of addition of…
In this paper, we introduce a new concept of rapidity and define formulae for energy and momentum as functions of the new rapidity, we denominate "counter-rapidity". The correspoding velocity is measured from the state of light speed in…
A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
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 concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If…
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…
The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal…