# Non-smooth mechanics

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**Non-smooth mechanics** is a modeling approach in mechanics which does not require the time evolutions of the positions and of the velocities to be smooth functions anymore. Due to possible impacts, the velocities of the mechanical system are even allowed to undergo jumps at certain time instants in order to fulfill the kinematical restrictions. Consider for example a rigid model of a ball which falls on the ground. Just before the impact between ball and ground, the ball has non-vanishing pre-impact velocity. At the impact time instant, the velocity must jump to a post-impact velocity which is at least zero, or else penetration would occur. Non-smooth mechanical models are often used in contact dynamics.

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## References[edit]

- Acary V., Brogliato, B. Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics.
*Springer Verlag, LNACM 35, Heidelberg, 2008.* - Brogliato B. Nonsmooth Mechanics. Models, Dynamics and Control.
*Communications and Control Engineering Series, Springer-Verlag, London, 2016 (3rd Ed.)* - Demyanov, V.F., Stavroulakis, G.E., Polyakova, L.N., Panagiotopoulos, P.D. Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics. Kluwer 1996, reprinted. Springer 2013
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- Glocker, Ch.
*Dynamik von Starrkoerpersystemen mit Reibung und Stoessen*, volume 18/182 of*VDI Fortschrittsberichte Mechanik/Bruchmechanik.*VDI Verlag, Düsseldorf, 1995 - Glocker Ch. and Studer C. Formulation and preparation for Numerical Evaluation of Linear Complementarity Systems.
*Multibody System Dynamics*13(4):447-463, 2005 - Haslinger, J., Stavroulakis, G.E. (eds), Nonsmooth Mechanics of Solids. CISM Lecture Notes, Springer 2006.
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*Computer Methods in Applied mechanics and Engineering*177(3-4):235-257, 1999 - Moreau J.J.
*Unilateral Contact and Dry Friction in Finite Freedom Dynamics,*volume 302 of*Non-smooth Mechanics and Applications, CISM Courses and Lectures*. Springer, Wien, 1988 - Pfeiffer F., Foerg M. and Ulbrich H. Numerical aspects of non-smooth multibody dynamics.
*Comput. Methods Appl. Mech. Engrg*195(50-51):6891-6908, 2006 - Potra F.A., Anitescu M., Gavrea B. and Trinkle J. A linearly implicit trapezoidal method for integrating stiff multibody dynamics with contacts, joints and friction.
*Int. J. Numer. Meth. Engng*66(7):1079-1124, 2006 - Stewart D.E. and Trinkle J.C. An Implicit Time-Stepping Scheme for Rigid Body Dynamics with Inelastic Collisions and Coulomb Friction.
*Int. J. Numer. Methods Engineering*39(15):2673-2691, 1996 - Studer C.
*Augmented time-stepping integration of non-smooth dynamical systems*, PhD Thesis ETH Zurich, ETH E-Collection, to appear 2008 - Studer C.
*Numerics of Unilateral Contacts and Friction -- Modeling and Numerical Time Integration in Non-Smooth Dynamics*, Lecture Notes in Applied and Computational Mechanics, Volume 47, Springer, Berlin, Heidelberg, 2009