Abstract
We consider a mechanical system with impact and one degree of freedom. The system is not necessarily Lagrangian. The representative point is subject to the constraint $u(t) \in \Er^+$ for all t. We assume that, at impact, the velocity is reversed and multiplied by a given coefficient of restitution $e\in[0,1]$. We define a numerical scheme which enables us to approximate the solutions of the Cauchy problem: this is an ad hoc scheme which does not require a systematic search for the times of impact. We prove the convergence of this numerical scheme to a solution. Many of the features of this proof will be reused in the nonconvex, multidimensional case, written in generalized coordinates, given in the companion paper [L. Paoli and M. Schatzman, SIAM J. Numer. Anal., 40 (2002), pp. 734--768]. We present some numerical results obtained with the scheme for a spring-dashpot system and we compare them to the results obtained by impact detection and penalization.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
