Abstract
We review several aspects of dynamics with impact with a finite number of degrees of freedom. We recall that the variational formulation has to be supplemented by a constitutive law for the impact. We take this law to be Newton’s law, with restitution coefficient r ∈ [0,1]. Dynamical problems have an intrinsic nonconvexity, due to the presence of second derivatives in time. Several results on the approximation of dynamics with impact are stated when the set of constraints is smooth. When the set of constraints is an angular domain, phenomena of ill-posedness are important. moreau’s rule for inelastic impact is justified by a penalty method.
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Paoli, L., Schatzman, M. (2001). Non Convex Aspects of Dynamics with Impact. In: Gilbert, R.P., Panagiotopoulos, P.D., Pardalos, P.M. (eds) From Convexity to Nonconvexity. Nonconvex Optimization and Its Applications, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0287-2_15
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DOI: https://doi.org/10.1007/978-1-4613-0287-2_15
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