Advice about the optimal coordination pattern for an individual speed skater to reach their optimal performance, could well be addressed by simulation and optimization of a biomechanical model of speed skating. But before getting to this optimization approach one needs a model that matches observed behavior. In this paper we present a simple 2-dimensional model of speed skating on the straights...

We consider the Savage-Hutter system consisting of two-dimensional depth-integrated shallow water equations for the incompressible fluid with the Coulomb-type friction term. Using the method of convex integration we show that the associated initial-value problem possesses infinitely many weak solutions for any finite-energy initial data. On the other hand, the problem enjoys the weak-strong uni...

This paper formally introduces several stability characterizations of £xtured three-dimensional rigid bodies initially at rest and in unilateral contact with Coulomb friction. These characterizations, weak stability and strong stability, arise naturally from the dynamic model of the system, formulated as a complementarity problem. Using the tools of complementarity theory, these characterizatio...

This paper introduces a hybrid scheme for simulating rigid bodies in contact. W e use (cm adaptive strategy for handling two different contact situations, 'bouncing' and 'steady'. To handle contact f o r rigid bodies, we use two impulse-based methods to explicitiy or implicitly compute impulses due to collision impact. These two methods are used so that different impulse methods are applied ada...

The present paper deals with shape optimization in discretized two-dimensional (2D) contact problems with Coulomb friction, where the coefficient of friction is assumed to depend on the unknown solution. Discretization of the continuous state problem leads to a system of finite-dimensional implicit variational inequalities, parametrized by the so-called design variable, that determines the shap...

The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical nonequilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a n...

For motion planning and veri cation as well as for model based control it is important to have an accurate dynamic system model In many cases friction is a signi cant component of the model When considering the solution of the rigid body forward dynamics problem in systems such as robots we can often appeal to the fundamental theorem of di erential equations to prove the existence and uniquenes...

Deformable systems that rely on dry friction for their proper functioning are widely found in many engineering applications such as bolted components, railway ballast. The design of these systems is usually considered from static point of view and employing Coulomb model of friction. This paper studies the effects of dynamic loading on the behavior of a two dimensional system by finite element ...

Elastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic–plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them – i.e....