Related papers: Skier and loop-the-loop with friction
An approximate analytical solution for the two body problem perturbed by a radial, low acceleration is obtained, using a regularized formulation of the orbital motion and the method of multiple scales. Formulating the dynamics with 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…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables…
The problem of the mechanical evolution of a shock between a cylindrically symmetric bat and a spherical ball is solved in the strict rigid approximation for arbitrary values of the initial conditions. The friction during the impact is…
We have studied the approach to equilibrium of islands and pores in two dimensions. The two-regime scenario observed when islands evolve according to a set of particular rules, namely relaxation by steps at low temperature and smooth at…
In this study, we present the phase-space analysis of Quintessence models specified by the choice of two potentials, namely the Recliner potential and what we call the broken exponential-law potential, which is a new proposal. Using a…
We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…
We propose event by event velocity fluctuations of nuclear fission fragments as an additional interesting observable that gives access to the nuclear temperature in an independent way from spectral measurements and relates the diffusion and…
It is usually believed that physics in off-equilibrium state characterized by hydrodynamic gradient can be equivalently studied using equilibrium state with suitable metric perturbation. We scrutinize this assumption using chiral kinetic…
We develop a spectral method for solving the incompressible generalized Navier--Stokes equations in the ball with no-flux and prescribed slip boundary conditions. The algorithm achieves an optimal complexity per time step of…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
One of the most fundamental questions in tribology concerns the area dependence of friction at the nanoscale. Here, experiments are presented where the frictional resistance of nanoparticles is measured by pushing them with the tip of an…
Quantum-mechanical system -- spin 1 particle in external Coulomb field is studied on the base of the matrix Duffin-Kemmer-Petiau formalism with the use of the tetrad technique. Separation of the variables is performed with the help of…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…
We perform a benchmark study of the step scaling procedure for the ratios of renormalization constants extracted from position space correlation functions. We work in the quenched approximation and consider the pseudoscalar, scalar, vector…
The case of the classical Hill problem is numerically investigated by performing a thorough and systematic classification of the initial conditions of the orbits. More precisely, the initial conditions of the orbits are classified into four…
We analyse the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and non-coagulating phases. We show that the phase transition is related to a Kramers problem, and use this to…
The phase diagram of the O(n) model, in particular the special case $n=0$, is studied by means of transfer-matrix calculations on the loop representation of the O(n) model. The model is defined on the square lattice; the loops are allowed…
We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…