V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems, Lecture Notes in Applied and Computational Mechanics, vol.35, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00423530

T. Arponen, Regularization of constraint singularities in multibody systems, Multibody System Dynamics, vol.6, issue.4, pp.355-375, 2001.
DOI : 10.1023/A:1012084517966

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

D. S. Bernstein, Matrix, Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory, 2005.

W. Blajer, Augmented Lagrangian formulation: geometrical interpretation and application to systems with singularities and redundancy, Multibody System Dynamics, vol.8, issue.2, pp.141-159, 2002.
DOI : 10.1023/A:1019581227898

B. Brogliato, Nonsmooth Mechanics, 1999.
DOI : 10.1007/978-1-4471-0557-2
URL : https://hal.archives-ouvertes.fr/hal-01236953

R. W. Cottle, On a Problem in Linear Inequalities, Journal of the London Mathematical Society, vol.1, issue.1, pp.378-384, 1968.
DOI : 10.1112/jlms/s1-43.1.378

R. W. Cottle, J. S. Pang, and R. E. Stone, The Linear Complementarity Problem, Computer Science and Scientific Computing, 1992.

E. Delassus, M??moire sur la th??orie des liaisons finies unilat??rales, Annales scientifiques de l'??cole normale sup??rieure, vol.34, pp.34-95, 1917.
DOI : 10.24033/asens.701

R. Dzonou, M. Marques, and M. D. , A sweeping process approach to inelastic contact problems with general inertia operators, European Journal of Mechanics - A/Solids, vol.26, issue.3, pp.474-490, 2007.
DOI : 10.1016/j.euromechsol.2006.07.002

R. Dzonou, M. Marques, M. D. Paoli, and L. , A convergence result for a vibro-impact problem with??a??general inertia operator, Nonlinear Dynamics, vol.2, issue.2, pp.1-2, 2009.
DOI : 10.1007/978-3-0348-7614-8
URL : https://hal.archives-ouvertes.fr/hal-01552482

F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Series in Operations Research, 2003.

M. Frémond, Non-smooth Thermomechanics, 2002.

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

C. Glocker, Set-Valued Force Laws: Dynamics of Non-smooth Systems, Lecture Notes in Applied and Computational Mechanics, vol.1, 2001.
DOI : 10.1007/978-3-540-44479-4

C. Glocker, Concepts for modeling impacts without friction, Acta Mechanica, vol.168, issue.1-2, pp.1-19, 2004.
DOI : 10.1007/s00707-004-0076-3
URL : http://www.zfm.ethz.ch/~glocker/publicationpdf/journal publications/bw_2004_actamechanica.pdf

C. Glocker, An Introduction to Impacts, Nonsmooth Mechanics of Solids. CISM Courses and Lectures, pp.45-102, 2006.
DOI : 10.1007/978-3-211-48243-8_2

C. Glocker and U. Aeberhard, The Geometry Of Newton???s Cradle, Nonsmooth Mechanics and Analysis. Theoretical and Numerical Advances. AMMA, pp.185-194, 2006.
DOI : 10.1007/0-387-29195-4_16

J. B. Hiriart-urruty and C. Lemaréchal, Fundamentals of Convex Analysis. Grundlehren Text Editions, 2001.
DOI : 10.1007/978-3-642-56468-0

P. Lancaster and M. Tismenetsky, The Theory of Matrices, 1985.

R. I. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-smooth Mechanical Systems, Lecture Notes in Applied and Computational Mechanics, vol.18, 2004.
DOI : 10.1007/978-3-540-44398-8

R. I. Leine and N. Van-de-wouw, Stability and Convergence of Mechanical Systems with Unilateral Constraints, Lecture Notes in Applied and Computational Mechanics, vol.36, 2008.
DOI : 10.1007/978-3-540-76975-0

R. I. Leine and N. Van-de-wouw, Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact, Nonlinear Dynamics, vol.43, issue.4, pp.551-583, 2008.
DOI : 10.1142/5442

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

M. Mabrouk, A unified variational model for the dynamics of perfect unilateral constraints, European Journal of Mechanics - A/Solids, vol.17, issue.5, pp.819-842, 1998.
DOI : 10.1016/S0997-7538(98)80007-7

N. H. Mcclamroch and D. Wang, Feedback stabilization and tracking of constrained robots, IEEE Transactions on Automatic Control, vol.33, issue.5, pp.419-426, 1988.
DOI : 10.1109/9.1220

M. Marques and M. D. , Differential Inclusions in Non-smooth Mechanical Problems: Shocks and Dry Friction, Birkhäuser, 1993.
DOI : 10.1007/978-3-0348-7614-8

J. J. Moreau, Les liaisons unilatérales et le principe de Gauss, C. R. Acad. Sci. Paris, vol.256, issue.4, pp.871-874, 1963.

J. 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

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

A. Müller, A Lie-group formulation of kinematics and dynamics of constrained MBS and its application to analytical mechanics, Multibody System Dynamics, vol.9, issue.4, pp.311-352, 2003.
DOI : 10.1023/A:1023321630764

A. Müller, A conservative elimination procedure for permanently redundant closure constraints in MBS-models with relative coordinates, Multibody System Dynamics, vol.14, issue.1, pp.309-330, 2006.
DOI : 10.1007/978-1-4757-2484-4

M. A. Neto and J. Ambrosio, Stabilization methods for the integration of DAE in the presence of redundant constraints, Multibody System Dynamics, vol.10, issue.1, pp.81-105, 2003.
DOI : 10.1023/A:1024567523268

Y. Or and E. Rimon, Investigation of Painlev?????s paradox and dynamic jamming during mechanism sliding motion, Nonlinear Dynamics, vol.75, issue.2, pp.1647-1668, 2012.
DOI : 10.1002/rnc.592

L. Paoli, CONTINUOUS DEPENDENCE ON DATA FOR VIBRO-IMPACT PROBLEMS, Mathematical Models and Methods in Applied Sciences, vol.359, issue.01, pp.1-41, 2005.
DOI : 10.1098/rsta.2001.0859

L. Paoli, Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. I: The Inelastic Impact Case, Archive for Rational Mechanics and Analysis, vol.359, issue.3, pp.457-568, 2010.
DOI : 10.1016/S0764-4442(00)88482-7
URL : https://hal.archives-ouvertes.fr/hal-01566929

L. Paoli, A proximal-like method for a class of second order measure-differential inclusions describing vibro-impact problems, Journal of Differential Equations, vol.250, issue.1, pp.476-514, 2011.
DOI : 10.1016/j.jde.2010.10.010
URL : https://hal.archives-ouvertes.fr/hal-01566931

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
URL : http://www.esaim-m2an.org/articles/m2an/pdf/1993/06/m2an1993270606731.pdf

F. Pfeiffer and C. Glocker, Multibody Dynamics with Unilateral Contacts, 1996.
DOI : 10.1002/9783527618385

R. T. Rockafellar, Convex Analysis, Princeton Landmarks in Mathematics, 1970.
DOI : 10.1515/9781400873173

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

W. J. Stronge, Impact Mechanics, 2000.
DOI : 10.1017/CBO9780511626432

C. Studer, Numerics of Unilateral Contacts and Friction: Modeling and Numerical Time Integration in Non-smooth Dynamics, Lecture Notes in Applied and Computational Mechanics, vol.47, 2009.
DOI : 10.1007/978-3-642-01100-9