V. Acary, Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts, Applied Numerical Mathematics, vol.62, issue.10, pp.1259-1275, 2012.
DOI : 10.1016/j.apnum.2012.06.026

URL : https://hal.archives-ouvertes.fr/inria-00476398

V. Acary, Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb???s friction, Computer Methods in Applied Mechanics and Engineering, vol.256, issue.1, pp.224-250, 2013.
DOI : 10.1016/j.cma.2012.12.012

V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics, Lecture Notes in Applied and Computational Mechanics, vol.35, 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/s10107-006-0041-0

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.3762

V. Acary, F. Cadoux, C. Lemaréchal, and J. Malick, A formulation of the linear discrete Coulomb friction problem via convex optimization, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.5, issue.4, pp.155-175, 2011.
DOI : 10.1002/zamm.201000073

URL : https://hal.archives-ouvertes.fr/inria-00495734

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

M. Anitescu, Optimization-based simulation of nonsmooth rigid multibody dynamics, Mathematical Programming, vol.65, issue.1, pp.113-143, 2006.
DOI : 10.1007/s10107-005-0590-7

M. Anitescu and F. A. Potra, Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems, Nonlinear Dynamics, vol.14, issue.3, pp.231-247, 1997.
DOI : 10.1023/A:1008292328909

M. Anitescu and A. Tasora, An iterative approach for cone complementarity problems for??nonsmooth dynamics, Computational Optimization and Applications, vol.117, issue.1, pp.207-235, 2010.
DOI : 10.1007/s10589-008-9223-4

M. Arnold and O. Brüls, Convergence of the generalized-?? scheme for constrained mechanical systems, Multibody System Dynamics, vol.85, issue.10, pp.185-202, 2007.
DOI : 10.1007/s11044-007-9084-0

URL : https://hal.archives-ouvertes.fr/hal-01490825

U. M. Ascher, H. Chin, L. R. Petzold, and S. Reich, Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds, Mechanics of Structures and Machines, vol.23, issue.2, pp.135-157, 1995.
DOI : 10.1016/0771-050X(80)90013-3

O. A. Bauchau and A. Laulusa, Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems, Journal of Computational and Nonlinear Dynamics, vol.3, issue.1, p.11005, 2007.
DOI : 10.1115/1.2803258

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

F. Bertails-descoubes, F. Cadoux, G. Daviet, and V. Acary, A nonsmooth Newton solver for capturing exact Coulomb friction in fiber assemblies, ACM Transactions on Graphics, vol.30, issue.1, pp.1-614, 2011.
DOI : 10.1145/1899404.1899410

URL : https://hal.archives-ouvertes.fr/inria-00557706

O. Bonnefon and G. Daviet, Quartic formulation of Coulomb 3D frictional contact, p.400, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00553859

B. Brogliato, Nonsmooth Mechanics: Models, Dynamics and Control, second edn, 1999.

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.39-61, 2015.
DOI : 10.1007/s11044-014-9437-4

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

A. Chatterjee, Rigid body collisions: Some general considerations, new collision laws, and some experimental data, 1997.

G. Daviet, F. Bertails-descoubes, and L. Boissieux, A hybrid iterative solver for robustly capturing coulomb friction in hair dynamics, ACM Transactions on Graphics, vol.30, issue.6, pp.1-13911, 2011.
DOI : 10.1145/2070781.2024173

URL : https://hal.archives-ouvertes.fr/hal-00647497

D. Saxcé, G. Feng, and Z. Q. , 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

D. Saxcé, G. Feng, and Z. Q. , The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms, Mathematical and Computer Modelling, vol.28, pp.4-8, 1998.

P. Flores, M. Machado, E. Seabra, and M. T. Da-silva, A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems, Journal of Computational and Nonlinear Dynamics, vol.6, issue.1, p.11019, 2011.
DOI : 10.1115/1.4002338

J. García-de-jalón and M. D. Gutiérrez-lópez, Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces, Multibody System Dynamics, vol.6, issue.3, pp.311-341, 2013.
DOI : 10.1007/s11044-013-9358-7

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 and F. Pfeiffer, Complementarity problems in multibody systems with planar friction, Archive of Applied Mechanics, vol.63, issue.7, pp.452-463, 1993.

M. Haddouni, V. Acary, and J. D. Beley, Comparison of index-3, index-2 and index-1 DAE solvers for nonsmooth multibody systems with unilateral and bilateral constraints, Proceedings of ECCOMAS Thematic Conference on Multibody Dynamics 2013, pp.133-142, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00821314

M. Jean, The non-smooth contact dynamics method, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.235-257, 1999.
DOI : 10.1016/S0045-7825(98)00383-1

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

P. Joli, N. Séguy, and Z. Q. Feng, A Modular Modeling Approach to Simulate Interactively Multibody Systems With a Baumgarte/Uzawa Formulation, Journal of Computational and Nonlinear Dynamics, vol.3, issue.1, p.11011, 2007.
DOI : 10.1115/1.2815331

URL : https://hal.archives-ouvertes.fr/hal-00342945

Y. Kanno, J. A. Martins, and A. Pinto-da-costa, Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem, International Journal for Numerical Methods in Engineering, vol.80, issue.1, pp.62-83, 2006.
DOI : 10.1002/nme.1493

R. Kikuuwe and H. Fujimoto, Incorporating Geometric Algorithms in Impedance- and Admittance-Type Haptic Rendering, Second Joint EuroHaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems (WHC'07), pp.249-254, 2007.
DOI : 10.1109/WHC.2007.75

R. Kikuuwe, N. Takesue, A. Sano, H. Mochiyama, and H. Fujimoto, Admittance and Impedance Representations of Friction Based on Implicit Euler Integration, IEEE Transactions on Robotics, vol.22, issue.6, pp.1176-1188, 2006.
DOI : 10.1109/TRO.2006.886262

Y. Kim, S. H. Kim, and Y. K. Kwak, Dynamic Analysis of a Nonholonomic Two-Wheeled Inverted Pendulum Robot, Journal of Intelligent and Robotic Systems, vol.49, issue.1, pp.25-46, 2005.
DOI : 10.1007/s10846-005-9022-4

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

M. Kobilarov, K. Crane, and M. Desbrun, Lie group integrators for animation and control of vehicles, ACM Transactions on Graphics, vol.28, issue.2, pp.1-1614, 2009.
DOI : 10.1145/1516522.1516527

R. I. Leine and C. Glocker, A Set-Valued Force Law for Spatial Coulomb-Contensou Friction, Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, pp.193-216, 2003.
DOI : 10.1115/DETC2003/VIB-48426

R. I. Leine, D. H. Van-campen, and C. Glocker, Nonlinear Dynamics and Modeling of Various Wooden Toys with Impact and Friction, Journal of Vibration and Control, vol.9, issue.1-2, pp.25-78, 2003.
DOI : 10.1177/107754603030741

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

W. Marquis-favre, E. Bideaux, and S. Scavarda, A planar mechanical library in the AMESim simulation software. Part I: Formulation of dynamics equations, Simulation Modelling Practice and Theory, vol.14, issue.1, pp.25-46, 2006.
DOI : 10.1016/j.simpat.2005.02.006

URL : https://hal.archives-ouvertes.fr/hal-00140638

H. Mazhar, T. Heyn, A. Pazouki, D. Melanz, A. Seidl et al., CHRONO: a parallel multi-physics library for rigid-body, flexible-body, and fluid dynamics, Mechanical Sciences, vol.4, issue.1, pp.49-64, 2013.
DOI : 10.5194/ms-4-49-2013

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

S. Nakaoka, S. Hattori, F. Kanehiro, S. Kajita, and H. Hirukawa, Constraint-based dynamics simulator for humanoid robots with shock absorbing mechanisms, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.3641-3647, 2007.
DOI : 10.1109/IROS.2007.4399415

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 : 10.1007/s11071-011-0094-3

M. Payr and C. Glocker, Oblique Frictional Impact of a Bar: Analysis and Comparison of Different Impact Laws, Nonlinear Dynamics, vol.6, issue.4, pp.361-383, 2005.
DOI : 10.1007/s11071-005-8200-z

F. Pfeiffer, Unilateral problems of dynamics, Archive of Applied Mechanics (Ingenieur Archiv), vol.69, issue.8, pp.503-527, 1999.
DOI : 10.1007/s004190050240

URL : https://hal.archives-ouvertes.fr/hal-01395964

T. Schindler and V. Acary, Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook, Mathematics and Computers in Simulation, vol.95, pp.180-199, 2013.
DOI : 10.1016/j.matcom.2012.04.012

URL : https://hal.archives-ouvertes.fr/hal-00762850

T. Schwager and T. Pöschel, Coefficient of restitution and linear???dashpot model revisited, Granular Matter, vol.60, issue.534, pp.465-469, 2007.
DOI : 10.1007/s10035-007-0065-z

M. Silcowitz, S. Niebe, and K. Erleben, Interactive rigid body dynamics using a projected Gauss-Seidel subspace minimization method Computer Vision, Imaging and Computer Graphics, Theory and Applications Communications in Computer and Information Science, vol.229, pp.218-229, 2011.

P. Song, P. Kraus, V. Kumar, and P. Dupont, Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts, Journal of Applied Mechanics, vol.68, issue.1, pp.118-128, 2001.
DOI : 10.1115/1.1331060

D. E. Stewart and J. C. 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

W. J. Stronge, Smooth dynamics of oblique impact with friction, International Journal of Impact Engineering, vol.51, pp.36-49, 2013.
DOI : 10.1016/j.ijimpeng.2012.08.001

C. Studer and C. Glocker, Representation of Normal Cone Inclusion Problems in Dynamics Via Non-linear Equations, Archive of Applied Mechanics, vol.92, issue.3, pp.5-6, 2006.
DOI : 10.1007/s00419-006-0031-y

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

X. Xiong, R. Kikuuwe, and M. Yamamoto, A Differential Algebraic Method to Approximate Nonsmooth Mechanical Systems by Ordinary Differential Equations, Journal of Applied Mathematics, vol.32, issue.1, p.320276, 2013.
DOI : 10.1016/j.na.2005.04.033