Difference methods for differential inclusions: a survey

TL;DR: This paper presents rigorous results about rigid-body dynamics with Coulomb friction and impulses, which have come from several sources: "sweeping processes" and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.-L.

TL;DR: In this paper, a new time-stepping method for simulating systems of rigid bodies is given which incorporates Coulomb friction and inelastic impacts and shocks, which does not need to identify explicitly impulsive forces.

TL;DR: A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented and previous results in the literature are extended.

TL;DR: This paper introduces and studies the class of differential variational inequalities (DVIs) in a finite-dimensional Euclidean space, and establishes the convergence of such a procedure for solving initial-value DVIs.

TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

TL;DR: The Euler Method and its Generalizations Analysis of Runge-Kutta Methods General Linear Methods Bibliography.

TL;DR: The organization of NLPQL is discussed, including the formulation of the subproblem and the information that must be provided by a user, and the performance of different algorithmic options is compared with that of some other available codes.