Non-smooth mechanics
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{{Short description, Modeling approach in mechanics Non-smooth mechanics is a modeling approach in
mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...
which does not require the time evolutions of the positions and of the velocities to be
smooth function In mathematical analysis, the smoothness of a function (mathematics), function is a property measured by the number of Continuous function, continuous Derivative (mathematics), derivatives it has over some domain, called ''differentiability cl ...
s 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 Contact dynamics deals with the motion of multibody systems subjected to unilateral contacts and friction. Such systems are omnipresent in many multibody dynamics applications. Consider for example * Contacts between wheels and ground in vehicle ...
.


See also

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Contact dynamics Contact dynamics deals with the motion of multibody systems subjected to unilateral contacts and friction. Such systems are omnipresent in many multibody dynamics applications. Consider for example * Contacts between wheels and ground in vehicle ...
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Unilateral contact In contact mechanics, the term unilateral contact, also called unilateral constraint, denotes a mechanical constraint which prevents penetration between two rigid/flexible bodies. Constraints of this kind are omnipresent in non-smooth multibody d ...
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Jean Jacques Moreau Jean Jacques Moreau (31 July 1923 – 9 January 2014) was a French mathematician and mechanician. He normally published under the name J. J. Moreau. Moreau was born in Blaye. He received his doctorate in mathematics from the University of Paris, ...


References

*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", Springer 1996. * Yang Gao, David, Ogden, Ray W., Stavroulakis, Georgios E. (Eds.) "Nonsmooth/Nonconvex Mechanics Modeling, Analysis and Numerical Methods", Springer 2001 *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 *Jean M. The non-smooth contact dynamics method. ''Computer Methods in Applied mechanics and Engineering'' 177(3-4):235-257, 1999 * Mistakidis, E.S., Stavroulakis, Georgios E. "Nonconvex Optimization in Mechanics Algorithms, Heuristics and Engineering Applications by the F.E.M.", Springer, 1998 *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 Mechanics Dynamical systems