The classical problem of rebound is usually treated by assuming that the colliding bodies are rigid and that the coefficient of friction, ~ , is constant. Two contact states can be distinguished: slidinq, in which the ratio of friction force to normal force is equal to ~ , and rolling, in which the friction force is zero. If sliding gives way to rolling during impact, the friction force will fa...

We present a fast penetration depth estimation algorithm between deformable polyhedral objects. We assume the continuum of non-rigid models are discretized using standard techniques, such as finite element or finite difference methods. As the objects deform, the distance fields are deformed accordingly to estimate penetration depth, allowing enforcement of non-penetration constraints between tw...

We propose a general framework for the simulation of sounds produced by colliding physical objects in a virtual reality environment. The framework is based on the vibration dynamics of bodies. The computed sounds depend on the material of the body, its shape, and the location of the contact. This simulation of sounds allows the user to obtain important auditory clues about the objects in the si...

One of the most important parts of the qualitative theory in differential equations is the stability of solutions. The problem of stabilizing the solutions by imposing proper impulse controls is very important to many areas of the sciences and engineering. It is important, for instance, in pharmacokinetics, biotechnology, economics, chemical technology and others. We consider certain second ord...

This paper proposes a multi-objective genetic algorithm to optimize a manipulator trajectory. The planner has several objectives namely the minimization of the space and join arm displacements and the energy required in the trajectory, without colliding with any obstacles in the workspace. Simulations results are presented for robots with two and three degrees of freedom, considering the optimi...

For a surface traction t, acting on a region Γt of the boundary of a given body Ω supported on Γ0 ⊂ ∂Ω, we consider the infimum σ opt t = infσ {ess supx |σ(x)|} over all stress fields σ in equilibrium with t, i.e., the smallest essential bound on all conceivable stress fields. Using the space of LD-vector fields on Ω, we show that σ t is attainable by some stress field σ̂ and that σ opt t = sup ...

Introduction: Collisions between planetesimals at speeds of several kilometers per second were common during the early evolution of our Solar System [e.g. 1,2,3,4]. However, shock heating of planetesimals in such impacts has largely been dismissed as a substantial heat source because of the high impact velocity required to shock-heat significant volumes of non-porous rock [e.g. 5,6]. However, r...

We present an e cient algorithm for simulation of non-penetrating exible bodies with nonlinear elasticity. We use nite element methods to discretize the continuum model of non-rigid objects and the fast marching level set method to precompute a distance eld for each undeformed body. As the objects deform, the distance elds are deformed accordingly to estimate penetration depth, allowing enforce...