Related papers: Rigid body motion in special relativity
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
The notions of "motion" and "conserved quantities", if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions…
Handling substance-like physical quantities in the limits of special relativity theory we should make a net distinction between those which present a proper (rest) magnitude and those which have not. We show how the theory relates them via…
Relativistic equation of state and velocity comparable with the speed of light are included in consideration of a superfluid rotating in a cylindrical container. Minimizing the free energy, we derive the equation of motion. It admits an…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…
We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the…
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
Rigid body with rotors is a widespread mechanical system modeled after the direct product $SO(3)\times S^1\times S^1\times S^1$, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and…
The dynamics of extended bodies is a fundamental problem in any gravitational theory. In the case of General Relativity, this problem is under study since the theory was published. Several methods have been developed and different…
A famous result by Delort about the two-dimensional incompressible Euler equations is the existence of weak solutions when the initial vorticity is a diffuse bounded Radon measure with distinguished sign. In this paper we are interested in…
On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin…
In this paper we consider the motion of a rigid body immersed in a two dimensional unbounded incompressible perfect fluid with vorticity. We prove that when the body shrinks to a massless pointwise particle with fixed circulation, the…
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…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
This paper aims at studying the spin once again. The departure point is thus the Stern and Gerlach experimental results that can be described in a coherent way in the frame of quantum mechanics only. Instead, the relativistic mechanics…
This work explores a classical mechanical theory under two further assumptions: (a) there is a universal dry friction force (Aristotelian mechanics), and (b) the variation of the mass of a body due to wear is proportional to the work done…
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional…
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence…