V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems, Lecture Notes in Applied and Computational Mechanics, vol.35, pp.10-1007, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00423530

V. Acary, B. Brogliato, and D. Goeleven, Higher order Moreau???s sweeping process: mathematical formulation and numerical simulation, Mathematical Programming, vol.43, issue.4, pp.133-217, 2008.
DOI : 10.1007/BFb0109998

URL : http://www.inrialpes.fr/bipop/publis/AcBrGo2008MATHPROGA.pdf

K. Addi, B. Brogliato, and D. Goeleven, A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems: applications in electronics, Mathematical Programming, vol.167, issue.1, pp.31-6710, 2011.
DOI : 10.1515/9781400873173

L. X. Anh, Dynamics of Mechanical Systems with Coulomb Friction, Foundations of Mechanical Engineering, 2003.
DOI : 10.1007/978-3-540-36516-7

E. Bayo and R. Ledesma, Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamics, Nonlinear Dynamics, vol.14, issue.1-2, pp.113-13010, 1996.
DOI : 10.1007/978-3-642-50995-7

D. 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

S. Boyd and L. Vandenberghe, Convex Optimization, 2004.

B. Brogliato, Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems, Multibody System Dynamics, vol.2, issue.6, pp.289-325, 2013.
DOI : 10.1007/978-3-642-01100-9

URL : https://hal.archives-ouvertes.fr/hal-00825581

B. Brogliato, Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction, Multibody System Dynamics, vol.8, issue.5, pp.175-216, 2014.
DOI : 10.1137/S1064827596297227

URL : https://hal.archives-ouvertes.fr/hal-00762986

B. Brogliato and D. Goeleven, Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems, Multibody System Dynamics, vol.32, issue.2, pp.39-6110, 2015.
DOI : 10.1016/S0167-6911(97)00054-6

URL : https://hal.archives-ouvertes.fr/hal-01088286

B. Brogliato and L. Thibault, Existence and uniqueness of solutions for non-autonomous complementarity dynamical systems, J. Convex Anal, vol.17, pp.3-4, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00756226

O. Brüls and M. Arnold, Convergence of the generalized ? scheme for constrained mechanical systems, Multibody Syst. Dyn, vol.18, issue.2, pp.185-202, 2007.

X. Chen and S. Xiang, Perturbation Bounds of P-Matrix Linear Complementarity Problems, SIAM Journal on Optimization, vol.18, issue.4, pp.1250-1265, 2007.
DOI : 10.1137/060653019

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

A. Ten-dam, E. Dwarshuis, and J. Willems, The contact problem for linear continuous-time dynamical systems: a geometric approach, IEEE Transactions on Automatic Control, vol.42, issue.4, pp.458-472, 1997.
DOI : 10.1109/9.566656

D. Dopico, F. González, J. Cuadrado, and J. Kövecses, Determination of Holonomic and Nonholonomic Constraint Reactions in an Index-3 Augmented Lagrangian Formulation With Velocity and Acceleration Projections, Journal of Computational and Nonlinear Dynamics, vol.9, issue.4, p.41006, 2014.
DOI : 10.1115/1.4027671

F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Operations Research, vol.1, 2003.

J. Fraczek and M. Wojtyra, On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints, Mechanism and Machine Theory, vol.46, issue.3, pp.312-334, 2011.
DOI : 10.1016/j.mechmachtheory.2010.11.003

F. Génot and B. Brogliato, New results on Painlev?? paradoxes, European Journal of Mechanics - A/Solids, vol.18, issue.4, pp.653-67710, 1999.
DOI : 10.1016/S0997-7538(99)00144-8

C. Glocker, The Principles of d'Alembert, Jourdain, and Gauss in Nonsmooth Dynamics Part I: Scleronomic Multibody Systems, ZAMM, vol.78, issue.1, pp.21-37, 1998.
DOI : 10.1002/(SICI)1521-4001(199801)78:1<21::AID-ZAMM21>3.0.CO;2-W

URL : https://hal.archives-ouvertes.fr/hal-01379709

C. Glocker, Set-Valued Force Laws: Dynamics of Non-Smooth Systems, 2001.
DOI : 10.1007/978-3-540-44479-4

E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Series in Computational Mathematics, 1996.
DOI : 10.1007/978-3-642-05221-7

M. Hjiaj, G. De-saxcé, and Z. Mroz, A variational inequality-based formulation of the frictional contact law with a??non-associated sliding rule, European Journal of Mechanics - A/Solids, vol.21, issue.1, pp.49-59, 2002.
DOI : 10.1016/S0997-7538(01)01183-4

URL : https://hal.archives-ouvertes.fr/hal-00140254

J. Hurtado and A. Sinclair, Lagrangian mechanics of overparameterized systems, Nonlinear Dynamics, vol.63, issue.1, pp.201-212, 2011.
DOI : 10.1016/S0021-8928(99)00005-2

A. Ivanov, Singularities in the dynamics of systems with non-ideal constraints, Journal of Applied Mathematics and Mechanics, vol.67, issue.2, pp.185-192, 2003.
DOI : 10.1016/S0021-8928(03)90004-9

A. Izmailov, A. Kurennoy, and M. Solodov, Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption, Computational Optimization and Applications, vol.131, issue.1???2, pp.111-14010, 2014.
DOI : 10.1007/s10107-010-0345-y

A. Jain, Operational Space Inertia for Closed-Chain Robotic Systems, Journal of Computational and Nonlinear Dynamics, vol.9, issue.2, p.21015, 2014.
DOI : 10.1115/1.4025893

J. G. De-jalon, A. Callejo, and A. Hidalgo, Efficient Solution of Maggi???s Equations, Journal of Computational and Nonlinear Dynamics, vol.7, issue.2, p.21003, 2012.
DOI : 10.1115/1.4005238

J. G. De-jalon and M. Gutierrez-lopez, Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraints forces, Multibody Syst. Dyn, vol.30, issue.3, pp.311-34110, 2013.

E. Jones, T. Oliphant, and P. Peterson, SciPy: open source scientific tools for Python URL http://www.scipy.org/. [Online, pp.2016-2021, 2001.

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

A. Laulusa and O. Bauchau, Review of Classical Approaches for Constraint Enforcement in Multibody Systems, Journal of Computational and Nonlinear Dynamics, vol.3, issue.1, p.11004, 2008.
DOI : 10.1115/1.2803257

R. Leine, B. Brogliato, and H. Nijmeijer, Periodic motion and bifurcations induced by the Painlev?? paradox, European Journal of Mechanics - A/Solids, vol.21, issue.5, pp.869-896, 2002.
DOI : 10.1016/S0997-7538(02)01231-7

URL : http://www.zfm.ethz.ch/~leine/papers/Leine %26 Brogliato %26 Nijmeijer - Periodic Motion and Bifurcations Induced by the Painleve Paradox.pdf

R. 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

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

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

C. Lunk and B. Simeon, Solving constrained mechanical systems by the family of Newmark and ??-methods, ZAMM, vol.158, issue.13, pp.772-784, 2006.
DOI : 10.1002/zamm.200610285

M. Anitescu and F. A. Potra, A time-stepping method for stiff multibody dynamics with contact and friction, International Journal for Numerical Methods in Engineering, vol.10, issue.7, pp.753-784, 2002.
DOI : 10.1007/978-1-4612-1394-9

V. Matrosov and I. Finogenko, Right-hand solutions of the differential equations of dynamics for mechanical systems with sliding friction, Journal of Applied Mathematics and Mechanics, vol.59, issue.6, pp.837-844, 1995.
DOI : 10.1016/0021-8928(95)00116-6

V. M. Matrosov and I. Finogenko, The theory of differential equations which arise in the dynamics of a system of rigid bodies with Coulomb friction, Monogr. Acad. Nonlinear Sci., Adv. Nonlinear Sci, vol.2, pp.16-106, 2008.

J. Moreau, Les liaisons unilatérales et le principe de Gauss, C. R. Acad. Sci, vol.256, issue.4, 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

A. Murua, Partitioned half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, Computing, vol.66, issue.1, pp.43-61, 1997.
DOI : 10.1007/978-3-642-05221-7

D. Negrut, L. Jay, and N. Khude, A Discussion of Low-Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics, Journal of Computational and Nonlinear Dynamics, vol.4, issue.2, p.21008, 2009.
DOI : 10.1115/1.3079784

P. Painlevé, Leçons sur le Frottement, 1895.

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/BFb0120929

J. Pang, J. Trinkle, and G. Lo, A complementarity approach to a quasistatic multi-rigid-body contact problem, Computational Optimization and Applications, vol.11, issue.2, pp.139-154, 1996.
DOI : 10.1109/70.370504

URL : http://www.cs.tamu.edu/faculty/trink/Papers/coap95PangTrinkLo.ps.Z

F. Pfeiffer, On non-smooth multibody dynamics, Proc. Inst, pp.147-177, 2012.
DOI : 10.1016/S0921-8890(96)00043-7

R. T. Rockafellar, Convex Analysis, pp.10-1142, 1970.
DOI : 10.1515/9781400873173

B. Ruzzeh and J. Kövecses, A Penalty Formulation for Dynamics Analysis of Redundant Mechanical Systems, Journal of Computational and Nonlinear Dynamics, vol.6, issue.2, p.21008, 2011.
DOI : 10.1115/1.4002510

G. De-saxcé and Z. Feng, New Inequality and Functional for Contact with Friction: The Implicit Standard Material Approach???, Mechanics of Structures and Machines, vol.273, issue.3, pp.301-325, 1991.
DOI : 10.1016/0045-7949(80)90146-7

A. Van-der-schaft and J. Schumacher, Complementarity modeling of hybrid systems, IEEE Transactions on Automatic Control, vol.43, issue.4, pp.483-490, 1998.
DOI : 10.1109/9.664151

A. Shabana, Euler parameters kinetic singularity, Proc. Inst, pp.10-1177, 2014.
DOI : 10.1007/978-3-642-86464-3

B. Simeon, Computational Flexible Multibody Dynamics. A Differential-Algebraic Approach Differential-Algebraic Equations Forum, 2013.
DOI : 10.1007/978-3-642-35158-7

Z. Terze, A. Müller, and D. Zlatar, Lie-group integration method for constrained multibody systems in state space, Multibody System Dynamics, vol.357, issue.1???2, pp.275-30510, 2015.
DOI : 10.1098/rsta.1999.0360

F. Udwadia and R. Kalaba, Analytical Dynamics: A New Approach, 1996.
DOI : 10.1017/CBO9780511665479

F. Udwadia and P. Phohomsiri, Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics, Proc. R. Soc. Lond. A 462, pp.2097-2117, 2006.
DOI : 10.1098/rspa.2006.1662

URL : https://hal.archives-ouvertes.fr/hal-01395968

F. Udwadia and A. Schutte, Equations of motion for general constrained systems in Lagrangian mechanics, Acta Mechanica, vol.36, issue.1-2, pp.111-129, 2010.
DOI : 10.1115/1.3260722

URL : https://hal.archives-ouvertes.fr/hal-01395969

M. Wojtyra, Joint reactions in rigid body mechanisms with dependent constraints, Mechanism and Machine Theory, vol.44, issue.12, pp.2265-2278, 2009.
DOI : 10.1016/j.mechmachtheory.2009.07.008

M. Wojtyra and J. Fraczek, Comparison of Selected Methods of Handling Redundant Constraints in Multibody Systems Simulations, Journal of Computational and Nonlinear Dynamics, vol.8, issue.2, p.210007, 2013.
DOI : 10.1115/1.4006958

M. Wojtyra and J. Fraczek, Solvability of reactions in rigid multibody systems with redundant nonholonomic constraints, Multibody System Dynamics, vol.8, issue.2, pp.153-171, 2013.
DOI : 10.1016/j.mechmachtheory.2009.07.008