Non-smooth mechanics is a modeling approach in

mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...

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 is a property measured by the number of continuous derivatives (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; t ...

s. Due to possible impacts, the velocities of the mechanical system are 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 d ...

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 {{Refs Mechanics Dynamical systems

See also

References