Related papers: The Precessing Top
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…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…
This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness of centrally symmetric polytopes and the…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
We present a new simple relativistic model for planetary motion describing accurately the anomalous precession of the perihelion of Mercury and its origin. The model is based on transforming Newton's classical equation for planetary motion…
We examine the problem of motion of an oscillating mass object provided no external force is applied to it. Calculations directly lead to the conclusion that the body accelerates in each system of reference except for the rest reference…
We consider normal velocity of smooth sets evolving by the $s-$fractional diffusion. We prove that for small time, the normal velocity of such sets is nearly proportional to the mean curvature of the boundary of the initial set for $s\in…
We consider the solid-solid interactions in the two body problem. The relative equilibria have been previously studied analytically and general motions were numerically analyzed using some expansion of the gravitational potential up to the…
The small discrepancy between the observed orbit of Mercury and the orbit predicted by Newtonian gravity was a key test of Einstein's theory, and a dramatic verification of the correctness of General Relativity. This `anomalous precession'…
We give a straightforward and divergence free derivation of the equation of motion for a small but finite object in an arbitrary background using strong field point particle limit. The resulting equation becomes a generalized geodesic for a…
The shape of a rotating star consisting of equilibrium plasma is considered. The velocity of apsidal rotation of close binary stars (periastron rotation) which depends on the star shapes is calculated. The obtained estimations are in a good…
In this paper we present a semantic study of motion complexes (ie. of a motion verb followed by a spatial preposition). We focus on the spatial and the temporal intrinsic semantic properties of the motion verbs, on the one hand, and of the…
The symmetric top is a special case of the general top, and canonical Poisson structure on $T^*SE(3)$ is the common method of its description. This structure is invariant under the right action of $SO(3)$, but the Hamiltonian of the…
By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as…
The behaviour of periodic points of discrete Euler top is studied. We derive invariant varieties of periodic points explicitly. When the top is axially symmetric they are specified by some particular values of the angular velocity along the…
The paper is based on the recently proposed 4-dimensional optical space theory and draws some of its consequences for gravitation. Starting with the discussion of central movement, the paper proceeds to establish the a metric compatible…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
A new path equation in absolute parallelism (AP) geometry is derived. The equation is a generalization of three path equations derived in a previous work. It can be considered as a geodesic equation modified by a torsion term, whose…
Random motions on the line and on the plane with space-varying velocities are considered and analyzed in this paper. On the line we investigate symmetric and asymmetric telegraph processes with space-dependent velocities and we are able to…
We determine the symmetrized topological complexity of the circle, using primarily just general topology.