W. Schiehlen, Developing algorithms for efficient simulation of flexible space manipulator operations, IAF-94-A.4.032, 45th Congress of the Int Astronautical Federation The scenario management tool SMARTFED for real-time interactive high performance networked simulations, High-Performance Computing and Networking, Multibody system dynamics: Roots and perspectives Israel. 23 van Sterkenburg RP and ten Dam AA 1999 Proc 7th Int Conf HPCN Europe 99, pp.149-188, 1994.

A. Chatterjee and A. Ruina, Two Interpretations of Rigidity in Rigid-Body Collisions, Journal of Applied Mechanics, vol.65, issue.4, pp.894-901, 1997.
DOI : 10.1115/1.2791929

E. Hairer and G. Wanner, Solving Ordinary Differential Equations II; Stiff and Differential-Algebraic Problems, Series in Computational Mathematics, 1996.

J. Garcia-de-jalon and E. Bayo, Kinematic and Dynamic Simulation of Multibody Systems: The Real-time Challenge, Mechanical Engineering Series, 1994.
DOI : 10.1007/978-1-4612-2600-0

P. Lötstedt, Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics, SIAM Journal on Scientific and Statistical Computing, vol.5, issue.2, pp.370-393, 1984.
DOI : 10.1137/0905028

J. Moreau, Dynamique de systèmes a ` liaisons unilatérales avec frottement sec e ´ventuel; essais numériques, 1986.

K. Brenan, S. Campbell, and L. Petzold, Numerical Solutions of Initial-Value Problems in Differential-Algebraic Equations, Convex Analysis, Princeton Landmarks in Mathematics, 1970.
DOI : 10.1137/1.9781611971224

A. Bressan, Questioni di regolarita e di unicita del moto in presenza di vincoli olonomi unilaterali, Rend. Sem. Mat. Univ. Padova, vol.29, pp.271-315, 1959.

M. Monteiro-marques, Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, 1993.

D. Stewart, Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlev??'s Problem, Archive for Rational Mechanics and Analysis, vol.145, issue.3, pp.215-260, 1998.
DOI : 10.1007/s002050050129

D. Stewart, Existence of solutions to rigid body dynamics and the Painlev?? paradoxes, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.325, issue.6, pp.689-693, 1997.
DOI : 10.1016/S0764-4442(97)84784-2

M. Mabrouk, A unified variational model for the dynamics of perfect unilateral constraints, Eur, J. Mech. A/Solids, vol.175, pp.819-842, 1998.

M. Mabrouk, Liaisons unilat??rales et chocs ??lastiques quelconques: un r??sultat d'existence, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.11, pp.1353-1357, 1998.
DOI : 10.1016/S0764-4442(98)80193-6

M. Carriero, E. Pascali, T. , R. Bolletino, and U. M. , Uniqueness of the one-dimensional bounce problem as a generic property in L 1, pp.61-87, 1982.

M. Carriero and E. Pascali, Uniqueness for the elastic onedimensional bounce problem, Proc of Nonlinear Variational Problems , Res. Notes Math, vol.127, pp.88-91, 1985.

W. Heemels, Linear Complementarity Systems: A study in hybrid dynamics The Netherlands, 1999.

W. Heemels, J. Schumacher, and S. Weiland, Linear complementarity systems, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math, vol.604, pp.1234-1269, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00834580

A. Van-der-schaft and J. Schumacher, Complementarity modeling of hybrid systems CWI Report, Dept Operations Research, Statistics and Systems Theory, BS-R9611, NL. Also in IEEE Trans. Autom. Control, vol.434, pp.483-490, 1998.

A. Van-der-schaft and J. Schumacher, An Introduction to Hybrid Dynamical Systems, 2000.
DOI : 10.1007/BFb0109998

P. Lötstedt, Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints, SIAM Journal on Applied Mathematics, vol.42, issue.2, pp.281-296, 1982.
DOI : 10.1137/0142022

D. Percivale, Uniqueness in the elastic bounce problem, Journal of Differential Equations, vol.56, issue.2, pp.206-215, 1985.
DOI : 10.1016/0022-0396(85)90105-6

URL : https://hal.archives-ouvertes.fr/hal-01294061

D. Percivale, Uniqueness in the elastic bounce problem, II, Journal of Differential Equations, vol.90, issue.2, pp.304-315, 1991.
DOI : 10.1016/0022-0396(91)90150-8

D. Percivale, Bounce problem with weak hypotheses of regularity, Annali di Matematica Pura ed Applicata, vol.2, issue.3, pp.259-274, 1986.
DOI : 10.1007/BF01769220

G. Buttazo and D. Percivale, The bounce problem on n-dimensional Riemannian manifolds, Atti. Accad. Naz. Lincei, Cl, 1981.

G. Buttazo and D. Percivale, On the approximation of the elastic bounce problem on Riemannian manifolds, Journal of Differential Equations, vol.47, issue.2, pp.227-245, 1983.
DOI : 10.1016/0022-0396(83)90035-9

P. Ballard, The Dynamics of Discrete Mechanical Systems with Perfect Unilateral Constraints, Archive for Rational Mechanics and Analysis, vol.154, issue.3, pp.199-274, 2000.
DOI : 10.1007/s002050000105

URL : https://hal.archives-ouvertes.fr/hal-00111308

P. Ballard, Dynamique des syst??mes m??caniques discrets avec liaisons unilat??rales parfaites, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics-Physics-Astronomy, vol.327, issue.10, pp.953-958, 1999.
DOI : 10.1016/S1287-4620(00)87003-9

M. Schatzman, A class of nonlinear differential equations of second order in time, Nonlinear Analysis: Theory, Methods & Applications, vol.2, issue.3, pp.355-373, 1978.
DOI : 10.1016/0362-546X(78)90022-6

URL : https://hal.archives-ouvertes.fr/hal-01294058

M. Schatzman, Uniqueness and continuous dependence on data for one-dimensional impact problems, Mathematical and Computer Modelling, vol.28, issue.4-8, pp.284-292, 1998.
DOI : 10.1016/S0895-7177(98)00104-6

L. Paoli and M. Schatzman, Mouvement ?? un nombre fini de degr??s de libert?? avec contraintes unilat??rales : cas avec perte d'??nergie, ESAIM: Mathematical Modelling and Numerical Analysis, vol.27, issue.6, pp.673-717, 1993.
DOI : 10.1051/m2an/1993270606731

L. Paoli, Analyse numérique de vibrations avec contraintes unilatérales, 1993.

L. Paoli and M. Schatzman, A numerical scheme for impact problems, preprint de l'Equipe d'Analyse Numérique, SIAM on Numerical Analysis, vol.5585, p.56, 1999.

L. Paoli and M. Schatzman, Approximation et existence en vibro-impact, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.329, issue.12, pp.1103-1107, 1999.
DOI : 10.1016/S0764-4442(00)88482-7

L. Paoli, AN EXISTENCE RESULT FOR VIBRATIONS WITH UNILATERAL CONSTRAINTS, Mathematical Models and Methods in Applied Sciences, vol.10, issue.06, 2000.
DOI : 10.1142/S0218202500000422

A. Ivanov, On multiple impact, Journal of Applied Mathematics and Mechanics, vol.59, issue.6, pp.930-946, 1995.
DOI : 10.1016/0021-8928(95)00122-0

M. Schatzman, C. Lamarque, and B. , An ill-posed mechanical problem with friction, European Journal of Mechanics - A/Solids, vol.18, issue.3, pp.415-420, 1999.
DOI : 10.1016/S0997-7538(99)00134-5

URL : https://hal.archives-ouvertes.fr/hal-00814941

D. Hilding, A. Klarbring, and J. Peterson, Optimization of Structures in Unilateral Contact, Applied Mechanics Reviews, vol.52, issue.4, pp.139-160, 1999.
DOI : 10.1115/1.3098931

R. Featherstone, Robot Dynamics Algorithms, 1987.

R. Wehage and E. Haug, Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems, Journal of Mechanical Design, vol.104, issue.1, pp.247-255, 1982.
DOI : 10.1115/1.3256318

D. Baraff, Linear-time dynamics using Lagrange multipliers, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques , SIGGRAPH '96, pp.137-146, 1996.
DOI : 10.1145/237170.237226

S. Mattsson, M. Otter, and E. , Modelica hybrid modeling and efficient simulation, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), pp.3502-3507, 1999.
DOI : 10.1109/CDC.1999.827881

A. Dam, Stable numerical integration of dynamical systems subject to equality state-space constraints, Journal of Engineering Mathematics, vol.11, issue.4, pp.315-337, 1997.
DOI : 10.1007/BF00042726

C. Gear, B. Leimkuhler, and G. Gupta, Automatic integration of Euler-Lagrange equations with constraints 12-13, 77-90. 68 ten Dam AA, Dwarshuis KF, and Willems JC 1997, The contact problem for linear continuous-time dynamical systems, a geometric approach, J. Comput. Appl. Math IEEE Trans. Autom. Control, vol.424, pp.458-472, 1985.

E. Delassus, Sur les lois du frottement de glissement, Bulletin de la Société mathématique de France, vol.2, pp.22-33, 1923.
DOI : 10.24033/bsmf.1029

J. Moreau, Les liaisons unilatérales et le principe de Gauss, C. R. Acad. Sciences Paris, vol.256, pp.871-874, 1963.

J. Moreau, Quadratic Programming in Mechanics: Dynamics of One-Sided Constraints, SIAM Journal on Control, vol.4, issue.1, pp.153-158, 1966.
DOI : 10.1137/0304014

URL : https://hal.archives-ouvertes.fr/hal-01379713

C. Gear and L. Petzold, ODE Methods for the Solution of Differential/Algebraic Systems, SIAM Journal on Numerical Analysis, vol.21, issue.4, pp.716-728, 1984.
DOI : 10.1137/0721048

A. Ivanov, Impacts in a system with certain unilateral couplings, Journal of Applied Mathematics and Mechanics, vol.51, issue.4, pp.559-566, 1987.
DOI : 10.1016/0021-8928(87)90081-5

L. Paoli and M. Schatzman, Moreau???s Rule and The Penalty Method, Proc of IUTAM Symp on Unilateral Multibody Contacts, pp.35-44, 1999.
DOI : 10.1007/978-94-011-4275-5_4

L. Paoli and M. Schatzmann, Penalty Approximation for Non-smooth Constraints in Vibroimpact, Journal of Differential Equations, vol.177, issue.2, pp.375-418, 2001.
DOI : 10.1006/jdeq.2001.4027

URL : https://hal.archives-ouvertes.fr/hal-00127048

L. Carnot, Principes Fondamentaux de l'Equilibre et du Mouvement

A. Chatterjee, On the realism of complementarity conditions in rigid body collisions, Nonlinear Dyn, pp.159-168, 1999.

J. Moreau, Some numerical methods in multibody dynamics: Application to granular materials, Eur, J. Mech. A/Solids, vol.134, pp.93-114, 1994.

A. Klarbring, A mathematical programming approach to three-dimensional contact problems with friction, Computer Methods in Applied Mechanics and Engineering, vol.58, issue.2, pp.175-200, 1986.
DOI : 10.1016/0045-7825(86)90095-2

A. Klarbring and G. Björkman, A mathematical programming approach to contact problems with friction and varying contact surface, Computers & Structures, vol.30, issue.5, pp.1185-1198, 1988.
DOI : 10.1016/0045-7949(88)90162-9

Y. Lootsma, A. Van-der-schaft, and C. Mk, Uniqueness of solutions of relay systems, Automatica, vol.353, pp.467-478, 1999.

J. Pang and J. Trinkle, Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction, Mathematical Programming, vol.14, issue.2, pp.199-226, 1996.
DOI : 10.1007/BF02592103

G. Ch, Formulation of spatial contact situations in rigid multibody systems, Comput. Methods Appl. Mech. Eng, vol.177, pp.199-214, 1999.

M. Anitescu, F. Potra, and D. Stewart, Time-stepping for three-dimensional rigid body dynamics, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.183-197, 1999.
DOI : 10.1016/S0045-7825(98)00380-6

D. Stewart and J. Trinkle, AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION, International Journal for Numerical Methods in Engineering, vol.61, issue.15, pp.2673-2691, 1996.
DOI : 10.1002/(SICI)1097-0207(19960815)39:15<2673::AID-NME972>3.0.CO;2-I

M. Anitescu, J. Cremer, and F. Potra, Formulating threedimensional contact dynamics problems, Mech. Struct. Mach, vol.864, 1996.

D. Stewart, Time stepping methods and the mathematics of rigid body dynamics, in Impact and Friction A Guran ed, 1999.

D. Stewart, Convergence of a time-stepping scheme for rigid body dynamics and resolution of Painlevé's problem; Summary, 1998.

J. Trinkle, J. Pang, S. Sudarsky, and G. Lo, On Dynamic Multi-Rigid-Body Contact Problems with Coulomb Friction, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.9, issue.4, pp.267-279, 1997.
DOI : 10.1002/zamm.19970770411

J. Pang and D. Stewart, A unified approach to discrete frictional contact problems, International Journal of Engineering Science, vol.37, issue.13, pp.1747-1768, 1999.
DOI : 10.1016/S0020-7225(98)00143-8

D. Stewart, Rigid-body dynamics with friction and impacts, SIAM Rev, pp.3-39, 2000.

M. Wösle and F. Pfeiffer, Dynamics of Multibody Systems Containing Dependent Unilateral Constraints with Friction, Journal of Vibration and Control, vol.2, issue.2, pp.161-192, 1996.
DOI : 10.1177/107754639600200203

M. Jean, The non-smooth contact dynamics method, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.235-277, 1999.
DOI : 10.1016/S0045-7825(98)00383-1

URL : https://hal.archives-ouvertes.fr/hal-01390459

J. Moreau, Unilateral Contact and Dry Friction in Finite Freedom Dynamics, pp.1-82, 1988.
DOI : 10.1007/978-3-7091-2624-0_1

M. Jean, Simulation numérique des problèmes de contact avec frottement, Matériaux et Techniques 1, pp.22-32, 1993.

J. Moreau, Liaisons unilatérales sans frottement et chocs ine ´lastiques, C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Terre Univers, pp.1473-1476, 1983.

C. Cholet, Chocs de solides rigides, 1998.

J. Moreau, Standard inelastic shocks and the dynamics of unilateral constraints, CISM Courses and Lectures, pp.173-221, 1985.

J. Moreau, Numerical aspects of the sweeping process, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.329-349, 1999.
DOI : 10.1016/S0045-7825(98)00387-9

URL : https://hal.archives-ouvertes.fr/hal-01349847

M. Kunze, M. Marques, and M. , An introduction to Moreau's sweeping process, In Impacts in Mechanical Systems: Analysis and Modeling, Lecture Notes in Physics, pp.1-60, 2000.

J. Moreau, Application of convex analysis to some problems of dry friction, Trends in Applications of Pure Mathematics to Mechanics, pp.263-280, 1979.

P. Panagiotopoulos, Modelling of nonconvex nonsmooth energy problems. Dynamic hemivariational inequalities with impact effects, Journal of Computational and Applied Mathematics, vol.63, issue.1-3, pp.123-138, 1995.
DOI : 10.1016/0377-0427(95)00050-X

A. Bressan, Incompatibilità dei teoremi di esistenza e di unicità del moto per un tipo molto comune e regolare di sistemi meccanici, Rend. Scu. Norm. di Pisa, pp.333-348, 1959.

Y. Hurmuzlu, An Energy-Based Coefficient of Restitution for Planar Impacts of Slender Bars With Massive External Surfaces, Journal of Applied Mechanics, vol.65, issue.4, pp.952-962, 1998.
DOI : 10.1115/1.2791939

Y. Hurmuzlu and V. Ceanga, Impulse correlation ratio in solving multiple impact problems, Impacts in Mechanical Systems: Analysis and Modeling, Lecture Notes in Physics, pp.235-273, 2000.

L. Paoli and M. Schatzman, Dynamics of an impacting bar: A model and numerics, ECCM'99, European Congress on Computational Mechanics, 1999.

R. Cottle, J. Pang, and R. Stone, The Linear Complementarity Problem, 1992.

M. Ferris and J. Pang, Engineering and economic applications of complementarity problems, SIAM Rev, pp.669-713, 1997.

R. Leine, G. Ch, and D. Van-campen, Nonlinear dynamics and modeling of some wooden toys with impact and friction, 2001.

F. Jourdan, P. Alart, and J. M. , A Gauss-Seidel like algorithm to solve frictional contact problems, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.1-2, pp.31-47, 1998.
DOI : 10.1016/S0045-7825(97)00137-0

M. Raous, P. Chabrand, and L. , Numerical methods for frictional contact problems and applications, J. Theo. Appl. Mech, vol.7, pp.111-128, 1988.

M. Raous, Quasistatic Signorini problem with Coulomb friction and coupling to adhesion, New Developments in Contact Problems , CISM 384, P Wriggers and P Panaglotiopoulos eds, 1999.

D. Vola, E. Pratt, M. Jean, and M. Raous, Consistent time discretization for a dynamical frictional contact problem and complementarity techniques, Revue Europ??enne des ??l??ments Finis, vol.7, issue.1-3, 1998.
DOI : 10.1080/12506559.1998.11690471

R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control: Theory and Applications Unilateral contacts in machine dynamics, 118 Schiehlen W 1999 Proc of IUTAM Symp on Unilateral Multibody Contacts, pp.287-298, 2000.
DOI : 10.1007/978-1-4471-3668-2

A. Rückgauer and W. Schiehlen, Simulation of modular mechatronic systems with application to vehicle dynamics, Acta Mech, pp.183-195, 1997.

P. Eberhard, Collision Detection and Contact Approaches for a hybrid Multibody System / Finite Element Simulation, Proc of IUTAM Symp on Unilateral Multibody Contacts, F Pfeiffer and Ch Glocker eds, pp.193-202, 1999.
DOI : 10.1007/978-94-011-4275-5_19

P. Ravn, A continuous analysis method for planar multibody systems with joint clearance, Multibody System Dynamics, vol.2, issue.1, pp.1-24, 1998.
DOI : 10.1023/A:1009759826529

P. Bliman and M. Sorine, Dry friction models for automatic control, Proc of Euromech Colloquium 351: Systems with Coulomb Friction, Vadstena Sweden, pp.5-7, 1996.

M. Sorine and J. Szymanski, A new dynamic multi dof tiremodel, IFAC Symp on Transportation Systems, pp.13-15, 2000.

L. Paoli and M. Schatzman, Non convex aspects of dynamics with impacts, From Convexity to Non Convexity, R Gilbert and P Pardalos eds, 2000.

P. Dupont and Y. Sp, Stability of rigid-body dynamics with sliding frictional contacts, Proceedings of IEEE International Conference on Robotics and Automation, pp.230-236, 1997.
DOI : 10.1109/ROBOT.1996.503806

L. Paoli and M. Schatzman, Ill-posedness in vibro-impact and its numerical consequences, European Congress on Computational Methods in Applied Sciences and Engineering, pp.11-14, 2000.

D. Baraff, Non-penetrating rigid body simulation, Eurograph- ics'93 State of the Art Reports, pp.6-10, 1993.

N. Hori, T. Morl, and P. Nikiforuk, Discrete-time models of continuous-time systems, Control and Dynamic Systems, pp.1-45, 1994.

K. Atkinson, An Introduction to Numerical Analysis, 1978.

J. Stoer and R. Burlisch, Introduction to Numerical Analysis, 1979.

J. Baumgarte, Stabilization of constraints and integrals of motion in dynamical systems, Computer Methods in Applied Mechanics and Engineering, vol.1, issue.1, pp.1-16, 1972.
DOI : 10.1016/0045-7825(72)90018-7

E. Bayo, J. Garcia-de-jalon, and M. Serna, A modified lagrangian formulation for the dynamic analysis of constrained mechanical systems, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.183-195, 1988.
DOI : 10.1016/0045-7825(88)90085-0

K. Park and J. Chiou, Stabilization of computational procedures for constrained dynamical systems, Journal of Guidance, Control, and Dynamics, vol.11, issue.4, pp.365-370, 1988.
DOI : 10.2514/3.20320

D. Sciacovelli, Flexible spacecraft: Computer oriented control analysis, Systems and Control Encyclopedia, pp.1649-1665, 1985.

E. Eich, Convergence Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints, SIAM Journal on Numerical Analysis, vol.30, issue.5, pp.1467-1482, 1993.
DOI : 10.1137/0730076

S. Campbell, Descriptor systems in the 90's, Proc of 29th Conf on Decision and Control, pp.442-447, 1990.

L. Petzold, A description of DASSL: A differential/algebraic system solver, Proc of 10th IMACS World Congress, 1982.

C. Führer and B. Leimkuhler, Formulation and numerical solution of the equations of constrained mechanical motion, DVFLR Forschungsbericht 89-08, 1989.

J. Baumgarte, A New Method of Stabilization for Holonomic Constraints, Journal of Applied Mechanics, vol.50, issue.4a, pp.869-870, 1983.
DOI : 10.1115/1.3167159

C. Chang and P. Nikravesh, An Adaptive Constraint Violation Stabilization Method for Dynamic Analysis of Mechanical Systems, Journal of Mechanisms Transmissions and Automation in Design, vol.107, issue.4, pp.488-492, 1985.
DOI : 10.1115/1.3260750

U. Asher, H. Chin, and R. , Stabilization of DAEs and invariant manifolds, Numerische Mathematik, vol.67, issue.2, pp.131-149, 1994.
DOI : 10.1007/s002110050020

S. Lin and M. Hong, Stabilization Method for Numerical Integration of Multibody Mechanical Systems, Journal of Mechanical Design, vol.120, issue.4, pp.565-572, 1998.
DOI : 10.1115/1.2829316

N. Mcclamroch and D. Wang, Linear Feedback Control of Position and Contact Force for a Nonlinear Constrained Mechanism, Journal of Dynamic Systems, Measurement, and Control, vol.112, issue.4, pp.640-645, 1990.
DOI : 10.1115/1.2896189

A. Veldman, ???Missing??? Boundary Conditions? Discretize First, Substitute Next, and Combine Later, SIAM Journal on Scientific and Statistical Computing, vol.11, issue.1, pp.82-91, 1990.
DOI : 10.1137/0911005

C. Hart and F. Harlow, A general corrective procedure for the numerical solution of initial-value problems, Journal of Computational Physics, vol.2, issue.2, pp.114-119, 1967.
DOI : 10.1016/0021-9991(67)90029-0

K. 146-gustafsson, M. Lundh, and O. , A PI step-size control for the numerical solution of ordinary differential equations, pp.270-287, 1988.

K. Gustafsson, Using control theory to improve step-size selection in numerical integration of ODE, 11th IFAC preprint, pp.139-144, 1990.

B. Von-herzen, A. Barr, and Z. Hr, Geometric collisions for time-dependent parametric surfaces, SIGGRAPH Conf Proc, pp.39-48, 1990.

A. Dam and J. Willems, A system theoretical framework to study unilaterally constrained dynamical systems, Proc of European Control Conf ECC'97, 1997.

Y. Wang, Global Analysis and Simulation of Mechanical Systems with Time-Varying Topologies, Journal of Mechanical Design, vol.115, issue.4, pp.817-821, 1993.
DOI : 10.1115/1.2919273

C. Lamarque and O. Janin, Mechanical systems with impacts: comparison of several numerical methods, Euromech Colloquium 397 Impact in Mechanical Systems, 1999.

O. Janin and C. Lamarque, Comparison of several numerical methods for mechanical systems with impacts, International Journal for Numerical Methods in Engineering, vol.51, issue.9, 1101.
DOI : 10.1002/nme.206

URL : https://hal.archives-ouvertes.fr/hal-00814950

O. Janin, Contribution a ` l'identification, la modèlisation et l'analyse de systèmes dynamiques a ` non-linéarites irrégulieres, 2001.

D. Towne and C. Hadlock, One???dimensional collisions and Chebyshev polynomials, American Journal of Physics, vol.45, issue.3, pp.255-259, 1977.
DOI : 10.1119/1.11003

F. Nqi, Etude numérique de divers problémes dynamiques avec impact et de leurs propriétés qualitatives, 1997.

D. Bainov and P. Simeonov, Systems with Impulse Effects, Theory and Applications, 1989.

M. Kunze and J. Neumann, Linear complementarity problems and the simulation of the motion of rigid body systems subject to Coulomb friction, Z. Angew. Math. Mech, vol.7711, pp.833-838, 1997.

W. Schmaedeke, Optimal Control Theory for Nonlinear Vector Differential Equations Containing Measures, Journal of the Society for Industrial and Applied Mathematics Series A Control, vol.3, issue.2, pp.231-280, 1965.
DOI : 10.1137/0303019

M. Camlibel, W. Heemels, and J. Schumacher, Dynamical analysis of linear passive networks with ideal diodes. Part II: Consistency of a time-stepping method, 2000.

D. Leenaerts, On linear dynamic complementarity systems, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl, vol.468, pp.1022-1026, 1999.

S. Wu, S. Yang, and E. Haug, Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion???II Planar systems, Mechanism and Machine Theory, vol.21, issue.5, pp.407-416, 1986.
DOI : 10.1016/0094-114X(86)90089-3

D. Wang, C. Conti, and B. , Interference Impact Analysis of Multibody Systems, Journal of Mechanical Design, vol.121, issue.1, pp.128-135, 1999.
DOI : 10.1115/1.2829413

J. Tzitzouris and J. Pang, A Time-Stepping Complementarity Approach for Frictionless Systems of Rigid Bodies, SIAM Journal on Optimization, vol.12, issue.3, 2001.
DOI : 10.1137/S1052623400370369

B. Mirtich, Impulse-based dynamic simulation of rigid body systems, 1997.

P. Hubbard, Approximating polyhedra with spheres for timecritical collision detection, ACM Trans. Graphics, vol.153, pp.181-210, 1996.

M. Ponamgi, D. Manosha, and L. Mc, Incremental algorithms for collision detection between solid models, Proceedings of the third ACM symposium on Solid modeling and applications , SMA '95, pp.293-304, 1995.
DOI : 10.1145/218013.218076

C. Conti, P. Corron, and P. Michotte, A computer-aided kinematic analysis system for mechanism design and computer simulation, Mechanism and Machine Theory, vol.27, issue.5, pp.563-574, 1992.
DOI : 10.1016/0094-114X(92)90045-J

S. Goyal, E. Pinson, and F. Sinden, Simulation of dynamics of interacting rigid bodies including friction I: General problem and contact model, Engineering with Computers, vol.29, issue.5, pp.162-174, 1994.
DOI : 10.1007/BF01198742

S. Goyal, E. Pinson, and F. Sinden, Simulation of dynamics of interacting rigid bodies including friction II: Software system design and implementation, Engineering with Computers, vol.18, issue.6, pp.175-195, 1994.
DOI : 10.1007/BF01198743

I. Han, B. Gilmore, and M. Ogot, The Incorporation of Arc Boundaries and Stick/Slip Friction in a Rule-Based Simulation Algorithm for Dynamic Mechanical Systems with Changing Topologies, Journal of Mechanical Design, vol.115, issue.3, pp.423-434, 1993.
DOI : 10.1115/1.2919207

D. Wang, C. Conti, P. Dehombreux, and O. Verlinden, A computer-aided simulation approach for mechanisms with timevarying topology, Comput. Struct, vol.6414, pp.519-530, 1997.

D. Filip, R. Magedson, and M. , Surface algorithms using bounds on derivatives, Computer Aided Geometric Design, vol.3, issue.4, pp.255-311, 1986.
DOI : 10.1016/0167-8396(86)90005-1

M. Lin and J. Canny, A fast algorithm for incremental distance calculation, Proceedings. 1991 IEEE International Conference on Robotics and Automation, pp.1008-1014, 1991.
DOI : 10.1109/ROBOT.1991.131723

J. Cohen, M. Lin, D. Manocah, and P. , I-Collide?An interactive and exact collision detection system for large scale environments, ACM Int 3D Graphics Conf, pp.112-120, 1995.

D. Baraff, Curved surfaces and coherence for non-penetrating rigid body simulation, ACM SIGGRAPH Computer Graphics, vol.24, issue.4, pp.19-28, 1990.
DOI : 10.1145/97880.97881

E. Allgower and G. K. , Numerical Continuation Methods: An Introduction, 1990.
DOI : 10.1137/1.9780898719154

P. Chabrand, F. Dubois, and M. Raous, Various numerical methods for solving unilateral contact problems with friction, Mathematical and Computer Modelling, vol.28, issue.4-8, pp.284-292, 1998.
DOI : 10.1016/S0895-7177(98)00111-3

URL : https://hal.archives-ouvertes.fr/hal-01393691

D. Baraff, Issues in computing contact forces for non-penetrating rigid bodies, Algorithmica, vol.22, issue.4, pp.292-352, 1993.
DOI : 10.1007/BF01891843

O. Mangasarian, Equivalence of the Complementarity Problem to a System of Nonlinear Equations, SIAM Journal on Applied Mathematics, vol.31, issue.1, 1976.
DOI : 10.1137/0131009

D. Leenaerts and W. Van-bokhoven, Piecewise Linear Modeling and Analysis, 1998.
DOI : 10.1007/978-1-4757-6190-0

M. Wösle and F. Pfeiffer, Formulations and solution methods of the dynamical spatial contact problem, Proc of IUTAM Symp on Unilateral Multibody Contacts, F Pfeiffer and Ch Glocker eds, pp.45-56, 1999.

M. Kojima, N. Megiddo, T. Noma, Y. A. Dubois, F. Raous et al., A unified Approach to Interior Point Algorithms for Linear Complementarity Problems, Programmation mathe ´matique pour le contact avec frottement et comparison avec d'autres méthodes, Deuxième Colloque National en Calcul des Structures, pp.16-20, 1991.

D. Baraff, Fast contact force computation for nonpentrating rigid bodies, Proc SIG-GRAPH'94, pp.23-34, 1994.

P. Christensen, A. Klarbring, J. Pang, and S. , Formulation and comparison of algorithms for frictional contact problems, International Journal for Numerical Methods in Engineering, vol.34, issue.1, pp.145-173, 1998.
DOI : 10.1002/(SICI)1097-0207(19980515)42:1<145::AID-NME358>3.0.CO;2-L

J. Pang and L. Qi, Nonsmooth Equations: Motivation and Algorithms, SIAM Journal on Optimization, vol.3, issue.3, pp.443-465, 1993.
DOI : 10.1137/0803021

N. Yamashita, Properties of Restricted NCP Functions for Nonlinear Complementarity Problems, Journal of Optimization Theory and Applications, vol.89, issue.3, pp.701-717, 1998.
DOI : 10.1023/A:1022684215427

F. Facchine and C. Kanzow, On Unconstrained and Constrained Stationary Points of the Implicit Lagrangian, Journal of Optimization Theory and Applications, vol.5, issue.1, pp.99-115, 1997.
DOI : 10.1023/A:1022688013571

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipies in Fortran, Contact mechanics in multibody systems, pp.665-675, 1992.

E. Wu, S. , and Y. Sm, 192 Simpack analysis and design of general mechanical systems Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion; I-theory, Mech, pp.401-406, 1986.

S. Wu, S. Yang, and E. Haug, Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint additiondeletion ; III-spatial systems, Mech. Mach. Theory, vol.215, pp.417-425, 1986.

I. Han and B. Gilmore, Multi-Body Impact Motion with Friction???Analysis, Simulation, and Experimental Validation, Journal of Mechanical Design, vol.115, issue.3, pp.412-422, 1993.
DOI : 10.1115/1.2919206

M. Pandy and N. Bermé, A numerical method for simulating the dynamics of human walking, Journal of Biomechanics, vol.21, issue.12, pp.1043-1051, 1998.
DOI : 10.1016/0021-9290(88)90250-3

P. Joli, M. Pascal, and J. Gibert, Systéme avec changement de topolgie dû a ` des liaisons de contact, Proc of 11th Congress Français de Mécanique, pp.429-432, 1993.

J. Escalona, J. Mayo, and D. , A new numerical method for the dynamic analysis of impact loads in flexible beams, Mechanism and Machine Theory, vol.34, issue.5, pp.765-780, 1999.
DOI : 10.1016/S0094-114X(98)00054-8

G. Ferretti, C. Maffezzoni, G. Magnani, and R. , Simulating discontinuous phenomena affecting robot motion, Journal of Intelligent and Robotic Systems, vol.33, issue.1, pp.53-65, 1996.
DOI : 10.1007/BF00435727

F. Génot and B. Brogliato, New results on Painlev?? paradoxes, European Journal of Mechanics - A/Solids, vol.18, issue.4, pp.653-677, 1999.
DOI : 10.1016/S0997-7538(99)00144-8

F. Génot, Contribution a ` la modélisation et a ` la commande des systémes mécaniques de corps rigides avec contraintes unilatérales, 1998.

P. Lötstedt, Coulomb Friction in Two-Dimensional Rigid Body Systems, ZAMM - Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.5, issue.12, pp.605-615, 1981.
DOI : 10.1002/zamm.19810611202

J. Moreau, La notion de sur-potentiel et les liaisons unilate ´rales en e ´lastostatique, pp.954-957, 1968.

J. Moreau, On unilateral constraints, friction and plasticity, New Variational Techniques in Mathematical Physics, CIME II ciclo 1973, G Capriz and G Stampacchia eds, Edizioni Cremonese, pp.175-322, 1974.

J. Moreau, Numerical Experiments in Granular Dynamics: Vibration-Induced Size Segregation, Proc of 2nd Contact Mechanics Int Symp, 1994.
DOI : 10.1007/978-1-4615-1983-6_47

F. Jourdan, M. Jean, and A. , An alternative method between implicit and explicit schemes devoted to frictional contact problems in deep drawing simulation, Journal of Materials Processing Technology, vol.80, issue.81, pp.80-81, 1998.
DOI : 10.1016/S0924-0136(98)00143-5

O. Chertier and P. Chabrand, Etude du frottement pour des problèmes de contact en grandes dèformations, Revue Européenne des Elements Finis, pp.71-73, 1998.

F. Pierrot, M. Jean, and D. , Nonsmooth mechanics approach for robot simulations, IFAC SYROCO, pp.577-582, 1994.

M. Jean and J. Moreau, Dynamics in the Presence of Unilateral Contacts and Dry Friction: A Numerical Approach, Unilateral Problems in Structural Analysis 2 CISM courses and lectures 304, pp.151-196, 1987.
DOI : 10.1007/978-3-7091-2967-8_10

A. Galka and J. Telega, Dynamic contact problems for systems with finite degrees of freedom: The case of piecewise regular constraints, Math. Comput. Modell, pp.284-292, 1998.

J. Kim and B. Kwak, Dynamic analysis of two-dimensional frictional contact by linear complementarity problem formulation, International Journal of Solids and Structures, vol.33, issue.30, pp.4605-4624, 1996.
DOI : 10.1016/0020-7683(95)00280-4

L. Johansson, A linear complementarity algorithm for rigid body impact with friction, Eur, J. Mech. A/Solids, vol.184, pp.703-717, 1999.

L. Johansson and A. Klarbring, Study of Frictional Impact Using a Nonsmooth Equations Solver, Journal of Applied Mechanics, vol.67, issue.2, pp.267-273, 2000.
DOI : 10.1115/1.1304825

P. Alart and A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods, Computer Methods in Applied Mechanics and Engineering, vol.92, issue.3, pp.353-375, 1991.
DOI : 10.1016/0045-7825(91)90022-X

J. Pang, Newton's Method for B-Differentiable Equations, Mathematics of Operations Research, vol.15, issue.2, pp.311-341, 1990.
DOI : 10.1287/moor.15.2.311

L. Paoli and M. Schatzman, Schéma numérique pour un modéle de vibrations avec contraintes unilatérales et perte d'e ´nergie aux impacts , en dimension finite, C. R. Acad. Sci., Ser. I: Math, vol.317, pp.211-215, 1993.

L. Paoli, M. Schatzman, and . Cd-rom, Theoretical and numerical study for vibrations with unilateral constraints: Case of a non-convex set of constraints, Proc 4th World Congress on Computational Mechanics, ?New Trends, and Applications, SR Idelsohn, E Onate, 1998.

J. Hubbard and B. West, Differential Equations: A Dynamical Systems Approach, Ordinary Differential Equations, 1991.

L. Paoli and M. Schatzman, Dynamical impact problem with loss of energy: Numerical study for large times Application to a model of tight joints, Proc of Contact Mechanics 95, pp.233-240, 1995.

M. Panet, L. Paoli, M. Schatzman, . Raous, and . Jean, Theoretical and Numerical Study for a Model of Vibrations with Unilateral Constraints, Contact Mechanics Int Symp JJ Moreau eds, vol.2, pp.19-23, 1994.
DOI : 10.1007/978-1-4615-1983-6_63

W. Bokhoven, Piecewise Linear Modelling and Analysis, 1981.

I. Sandberg, Theorems on the computation of the transient response of nonlinear networks containing transistors and diodes, Bell Syst, Tech. J, vol.49, pp.1739-1776, 1970.

A. Massarini, U. Reggiani, and K. Kazimierczuk, Analysis of networks with ideal switches by state equations, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.44, issue.8, pp.692-697, 1997.
DOI : 10.1109/81.611264

D. Bedrosian and J. Vlach, Time-domain analysis of networks with internally controlled switches, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl, vol.393, pp.199-212, 1992.

M. Lin and F. Canny, Efficient collision detection for animation, Third Eurographics Workshop on Animation and Simulation, 1992.

L. Suan, The Painlevé paradoxes and the law of motion of mechanical systems with Coulomb friction, Prikl. Math. Mekh. Transl. in J. Appl. Math. Mech, vol.544, issue.544, pp.520-529, 1990.

D. Stewart, Painlevé's problem and its implication for rigidbody dynamics, Euromech Colloquium 397 Impact in Mechanical Systems, 1999.

L. Wood and K. Byrne, Analysis of a random repeated impact process, Journal of Sound and Vibration, vol.78, issue.3, pp.329-345, 1981.
DOI : 10.1016/S0022-460X(81)80143-5

P. Holmes, The dynamics of repeated impacts with a sinusoidally vibrating table, Journal of Sound and Vibration, vol.84, issue.2, pp.173-189, 1982.
DOI : 10.1016/S0022-460X(82)80002-3

R. Brach and R. Brach, A Review of Impact Models for Vehicle Collision, SAE Technical Paper Series, 1987.
DOI : 10.4271/870048

F. Pfeiffer, . Glocker, J. Trinkle, and N. Amato, Unilateral multibody contacts Hybrid dynamic simulation of rigid-body contact with Coulomb friction, Proc of IUTAM Symp Proc of IEEE Int Conf on Robotics and Automation, 1998.

J. Moreau and P. , Nonsmooth Mechanics and Applications, CISM Courses and Lectures no 302, Int Centre for Mechanical Sciences, 1988.