Related papers: A Problem of Relative, Constrained Motion
We propose a polynomial force-motion model for planar sliding. The set of generalized friction loads is the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. Additionally, the polynomial is…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
We study the rheology of a granular material slowly driven in a confined geometry. The motion is characterized by a steady sliding with a resistance force increasing with the driving velocity and the surrounding relative humidity. For lower…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual…
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution…
It is argued that the `perspectival change' of a physical object in special relativity may be given a natural dynamical explanation in terms of a change in the object under the action of certain forces in a rest properties-preserving way.
In relativistic dynamics, force and acceleration are no longer parallel. In this article, we revisit the relativistic motion of a particle under the action of a constant force, $\boldsymbol{f}$. \ For a two-dimensional motion, the final…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…
As we move through the world, the pattern of light projected on our eyes is complex and dynamic, yet we are still able to distinguish between moving and stationary objects. We propose that humans accomplish this by exploiting constraints…
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
We show that the path of any accelerated body in an arbitrary space-time geometry $g_{\mu\nu}$ can be described as geodesics in a dragged metric $\hat{q}_{\mu\nu}$ that depends only on the background metric and on the motion of the body.…
An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…
An individual defect in a nematic liquid crystal moves not only in response to its interaction with other defects but also in response to an external field. We analyze the motion of a wedge disclination in the presence of an applied field…
The suppression of friction between sliding objects, modulated or enhanced by mechanical vibrations, is well established. However, the precise conditions of occurrence of these phenomena is not well understood. Here we address these…
In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solution is uniquely determined. How to incorporate obstacles,…
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…