Related papers: Brachistochrone of a Spherical Uniform Mass Distri…
If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by…
The Brachistochrone problem, which describes the curve that carries a particle under gravity in a vertical plane from one height to another in the shortest time, is one of the most famous studies in classical physics. There is a similar…
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical…
We analyze the motion of a particle in the gravity field along a family of differentiable curves taking into account the Coulomb friction forces. A parametric equation of the optimal curves is given that generalizes the cycloid one in this…
We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
Consider a frictionless surface S in a gravitational field that need not be uniform. Given two points A and B on S, what curve is traced out by a particle that starts at A and reaches B in the shortest time? This paper considers this…
The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant.…
The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
The general solution of Einstein's gravity equation in $D$ dimensions for an anisotropic and spherically symmetric matter distribution is calculated in a bulk with position dependent cosmological constant. Results for $n$ concentric…
The brachistochrone problem can be solved either by variational calculus or by a skillful application of the Snellius' law of refraction. This suggests the question whether also other variational problems can be solved by an analogue of the…
We propose a new test of Einstein's theory of gravitation. It concerns the velocity distribution of low-energy particles in a spherically symmetric gravitational field.
We consider the problem of finding paths of shortest transit time between two points (popularly known as Brachistochrone) for cylinders with off-centered center of mass, rolling down without slip, subject solely to the force of gravity.…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We consider different generalizations of the Brachistochrone Problem in the context of fundamental concepts of classical mechanics. The correct statement for the Brachistochrone problem for nonholonomic systems is proposed. It is shown that…
A precise solution of the general relativity equations for centrally symmetric distribution of a pseudoscalar field with U(1) symmetry is presented. It is found that energy density of the field is restricted in the symmetry center and falls…
We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle,…