Search results for "Non smooth"
showing 3 items of 3 documents
Non-smooth modelling of billiard- and superbilliard-ball collisions
2008
Abstract A description of billiard-ball collisions using a ‘discontinuous’ model is presented considering a two-step situation corresponding to the ball–ball interaction followed by ball-supporting surface interaction. It is applied to the inelastic impact of a cue ball having arbitrary pivotment and ‘English’ spins against an object ball initially at rest. This formulation provides a simplified approximation to the ‘continuous’ models of impact and considers two different regimes of impact: gross slip, and slip–stick, described in terms of coefficients of friction and restitution. As a result, the angles of scattering of the balls just after the impact (post-collision angles) and when the …
Coupled systems of non-smooth differential equations
2012
Abstract We study the geometric qualitative behavior of a class of discontinuous vector fields in four dimensions. Explicit existence conditions of one-parameter families of periodic orbits for models involving two coupled relay systems are given. We derive existence conditions of one-parameter families of periodic solutions of systems of two second order non-smooth differential equations. We also study the persistence of such periodic orbits in the case of analytic perturbations of our relay systems. These results can be seen as analogous to the Lyapunov Centre Theorem.
Corrigendum to “Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations” [19 (6) (2014) 1746–1769]
2015
Corrigendum Corrigendum to ‘‘Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations’’ [19 (6) (2014) 1746–1769] M. Russo , S. Roy Choudhury , T. Rehman , G. Gambino b University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., Orlando, USA University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123 Palermo, Italy