Related papers: The Existence and Uniqueness of Solutions to N-Bod…
Due to the finite speed of light, direct electrodynamic interaction between point charges can naturally be described by a system of ordinary differential equations involving delays. As electrodynamics is time-symmetric, these delays appear…
Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the…
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
We extend the canonical formalism for the motion of $N$-particles in lineal gravity to include charges. Under suitable coordinate conditions and boundary conditions the determining equation of the Hamiltonian (a kind of transcendental…
The Classical Newtonian problem of describing the free motions of N gravitating bodies which form an isolated system in free space has been considered. It is well known from the Poincares Dictum that the problem is not exactly solvable.…
Analysis of the original Feynman's formula for a moving point charge leads to the notion of a retarded time, which has to be treated as a field. The Lorentzian frame, the trajectory, and the retarded time field uniquely determine a system…
The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed…
Given the path of a point particle, one can relate its acceleration and, in general, its kinematics to the curvature scalars of its trajectory. Using this, a general Ansatz is made for the Yang Mills connection corresponding to a…
The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), of which the motion gives us general solutions of the three body problem. A…
Around 1930, both Gregory Breit and Erwin Schroedinger showed that the eigenvalues of the velocity of a particle described by wavepacket solutions to the Dirac equation are simply $\pm$c, the speed of light. This led Schroedinger to coin…
During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
We consider the Newtonian planar three-body problem, defining a syzygy (velocity syzygy) as a configuration where the positions (velocities) of the three bodies become collinear. We demonstrate that if the total energy is negative, every…
(Shortened due to character limit) This thesis consists of two parts. In part I we consider a discrepancy in the derivation of the electromagnetic self force for a point charge. In the point charge framework the self force can be defined as…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
Non-Hermitian quantum one-parametric $N$ by $N$ matrix Hamiltonians $H^{(N)}(\lambda)$ with real spectra are considered. Their special choice $H^{(N)}(\lambda)=J^{(N)}+\lambda\,V^{(N)}(\lambda)$ is studied at small $\lambda$, with a general…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…