相关论文: Brachistochrones With Loose Ends

The classical dynamics of particles with (non-)abelian charges and spin moving on curved manifolds is established in the Poisson-Hamilton framework. Equations of motion are derived for the minimal quadratic Hamiltonian and some extensions…

We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that…

The solution of the classic problem of stress in a rotating elastic disk or cylinder, as solved in standard texts on elasticity theory, has two features: dynamical equations are used that are valid only in an inertial frame of reference,…

We analyze a simple problem in elasticity: the \emph{initial} motion of an elastic bar that after being hanged from an end is suddenly released. In a second problem a point mass is attached on the top of the bar. The analytical solutions…

We examine the stick-slip fluctuating response of a rough massive non-rotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The…

We have devised an original laboratory experiment where we investigate the frictional behaviour of a single crystal salt slider over a large number of deformation cycles. Because of its physical properties, salt, a surrogate for natural…

Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary…

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…

We examined the asymmetric deformation in collisions and the transition conditions from oblique to normal collisions and non-collisions to address the problem of oblique collisions of rigid bodies in classical mechanics. A closed solution…

We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parametrizing the solutions in terms of an auxiliary time variable, which is a function only of the…

The classical solution of bosonic d-brane in (d+1,1) space-time is studied. We work with light-cone gauge and reduce the problem into Chaplygin gas problem. The static equation is equivalent to vanishing of extrinsic mean curvature, which…

In this paper, we explore the connections between Christiaan Huygens and Niels Henrik Abel through the tautochrone problem. The problem -- determining the curve along which a particle descends under gravity in the same time, regardless of…

The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise…

We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…

Problems involving rotating systems analyzed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. One of the problems that I…

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…

We prove an existence result for the Backus interior problem in the Euclidean ball. The problem consists in determining a harmonic function in the ball from the knowledge of the modulus of its gradient on the boundary. The problem is…

The breaking rate of an atomic chain stretched at zero temperature by a constant force can be calculated in a quasiclassical approximation by finding the localized solutions ("bounces") of the equations of classical dynamics in imaginary…

Inspired by a planar partitioning problem involving multiple improper chambers, this article investigates using classical techniques what can be said of the existence, uniqueness, and regularity of minimizers in a certain free-endpoint…

This study numerically investigated the friction of viscoelastic objects with grooves. A 3D viscoelastic block with grooves on a rigid substrate is slowly pushed from the lateral side under uniform pressure on the top surface. The local…