相关论文: Brachistochrones With Loose Ends

The classical Kramers problem of the kinetic theory is analytically solved. The Kramers problem about isothermal sliding for quantum Fermi gases is considered. Quantum gases with the velocity-dependent collision frequency are considered.…

Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through…

A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving…

We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This…

We solve the St.Venant torsion problem for an infinite cylindrical rod whose behaviour is described by a family of isotropic generalized continua, including the relaxed micromorphic and classical micromorphic model. The results can be used…

This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as…

In this paper we investigate the discrete version of the classical hanging chain problem. We generalize the problem, by allowing for arbitrary mass and length of each link. We show that the shape of the chain can be obtained by solving a…

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…

This paper presents an analytical framework to study the geometry arising when a soft continuum arm grasps a planar object. Both the arm centerline and the object boundary are modeled as smooth curves. The grasping problem is formulated as…

We present a detailed analysis of all possible regular precessions of a heavy asymmetric body with a fixed point not coinciding with the center of mass. The calculations are done in terms of the rotation matrix, by writing the Euler-Poisson…

Lambert's problem is a classical boundary value problem in analytical mechanics. It arises when trying to determine the energy required to place a particle, subject to a central gravitational potential, in a "free fall" trajectory…

One of classical boundary problems of the kinetic theory (a problem about thermal sliding) of the rarefied gas along a flat firm surface is considered. Kinetic Boltzmann equation with model integral of collisions BGK (Bhatnagar, Gross,…

The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…

Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…

We proceed from the fact that the classical paths of irreducible massive spinning particle lie on a circular cylinder with the time-like axis in Minkowski space. Assuming that all the classical paths on the cylinder are gauge-equivalent, we…

In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…

A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…

The lifting problem that we consider asks: given a smooth curve in characteristic p and a group of automorphisms, can we lift the curve, along with the automorphisms, to characteristic zero? One can reduce this to a local question (the…

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…

We describe the variation of the number $N(t)$ of spatial critical points of smooth curves (defined as a scalar distance $r$ from a fixed origin $O$) evolving under curvature-driven flows. In the latter, the speed $v$ in the direction of…