Related papers: The String Deviation Equation
Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three-dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of the…
We analyze the consequences of a recent argument justifying the validity of the "geodesic rule" which can be used to determine the density of global topological defects. We derive a formula that provides a rough estimate of the number of…
We reformulate two dimensional string-inspired gravity with point particles as a gauge theory of the extended Poincar\'e group. A non-minimal gauge coupling is necessary for the equivalence of the two descriptions. The classical…
A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space…
A point particle of small mass m moves in free fall through a background vacuum spacetime metric g_ab and creates a first-order metric perturbation h^1ret_ab that diverges at the particle. Elementary expressions are known for the singular…
The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a…
We extend the previous work of Olivier Costa de Beauregard regarding the isomorphism between the equation describing the motion of relativistic point particles and the equation describing the static equilibrium of classical elastic strings,…
The motion of charged particles in weakly varying electromagnetic fields is described using a perturbation method. This provides a systematic and physically transparent description of the particle motion on fast and slow spatio-temporal…
Employing a kinetic framework, we calculate all transport coefficients for relativistic dissipative (second-order) hydrodynamics for arbitrary particle masses in the 14-moment approximation. Taking the non-relativistic limit, it is shown…
The scientific question resolved by this paper is that the continuity equation appears as an equivalent language of the system of first-order linear ODE. The main result characterizes the fact that the continuity equation contains…
We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem…
The motion of spinning test-masses in curved space-time is described with a covariant hamiltonian formalism. A large class of hamiltonians can be used with the model- independent Poisson-Dirac brackets, to obtain equations of motion. Here…
The section condition in double field theory has been shown to imply that a physical point should be one-to-one identified with a gauge orbit in the doubled coordinate space. Here we show the converse is also true, and continue to explore…
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…
It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz…
The most general form of the deviation equations in spaces with linear connection with arbitrary torsion is derived.
The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…
A point particle of mass m moving on a geodesic creates a perturbation h, of the spacetime metric g, that diverges at the particle. Simple expressions are given for the singular m/r part of h and its quadrupole distortion caused by the…
We discovered that when a pair of small particles is optically levitated, the particles execute a dance whose motion resembles the orbits of balls being juggled. This motion lies in a plane perpendicular to the polarization of the incident…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.