相关论文: A mechanical model that exhibits a gravitational c…
We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…
We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…
A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
We consider a particle on the horizontal plane with a dry friction. The friction is anisotropic but symmetric under the group of rotations of the plane. It turns out that the particle can move such that in the finite time the trajectory…
The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model.…
We derive a theoretical model of mass and angular momentum scaling in type-II critical collapse with rotation. We focus on the case where the critical solution has precisely one, spherically symmetric, unstable mode. We demonstrate…
We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive…
Quantum field model of unstable particles with random mass is suggested to describe the finite-width effects in decay rate. Within the framework of this model we derive the convolution formula for a width of the channels with unstable…
A particle is thrown tangentially on a surface. It is shown that for some surfaces and for special initial velocities the thrown particle leaves immediately the surface, and for special conditions it never leaves the surface. The conditions…
Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the…
Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than…
When a soft elastic cylinder is bent beyond a critical radius of curvature, a sharp fold in the form of a kink appears at its inner side while the outer side remains smooth. The critical radius increases linearly with the diameter of the…
We use a simple model of particle shape to investigate how particle asymmetry affects particle-surface interaction, orientation, and stochastic dynamics over a planar surface. With this geometric model, we construct potential energy curves…
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…
A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the…
The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the…