M. P. Calvo and J. M. Sanz-serna, The development of variable-step symplectic integrators, with application to the two-body problem, SIAM J. Sci. Comput, vol.14, pp.936-952, 1993.

J. Chabassier and S. Imperiale, Introduction and study of fourth order theta schemes for linear wave equations, J. Comput. Appl. Math, vol.245, pp.194-212, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01051803

J. Chabassier and P. Joly, Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: Application to the vibrating piano string, Comput. Methods Appl. Mech. Eng, vol.199, issue.45, pp.2779-2795, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00444470

J. Diaz and M. J. Grote, Energy conserving explicit local time stepping for secondorder wave equations, SIAM J. Sci. Comput, vol.31, issue.3, pp.1985-2014, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00193160

R. C. Fetecau, J. E. Marsden, M. Ortiz, and M. West, Nonsmooth Lagrangian mechanics and variational collision integrators, SIAM J. Appl. Dyn. Syst, vol.2, issue.3, pp.381-416, 2003.

W. Fong, E. Darve, and A. Lew, Stability of asynchronous variational integrators, J. Comput. Phys, vol.227, issue.18, pp.8367-8394, 2008.

O. Gonzalez and J. C. Simo, On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry, Comput. Methods Appl. Mech. Eng, vol.134, issue.3-4, pp.197-222, 1996.

M. Groß, P. Betsch, and P. Steinmann, Conservation properties of a time FE method. part IV: Higher order energy and momentum conserving schemes, Int. J. Numer. Methods Eng, vol.63, issue.13, pp.1849-1897, 2005.

E. Hairer, Variable time step integration with symplectic methods, Appl. Numer. Math, vol.25, issue.2-3, pp.219-227, 1997.

E. Hairer, Energy-preserving variant of collocation methods, J. Numer. Anal. Industr. Appl. Math, vol.5, pp.73-84, 2010.

E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration: structurepreserving algorithms for ordinary differential equations, vol.31, 2006.

P. Hauret and P. L. Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Comput. Methods Appl. Mech. Eng, vol.195, issue.37, pp.4890-4916, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00111458

T. J. Hughes, W. K. Liu, and P. Caughy, Transient finite element formulations that preserve energy, J. Appl. Mech, vol.45, pp.366-370, 1978.

A. Iserles, H. Z. Munthe-kaas, S. P. Nørsett, and A. Zanna, Lie-group methods, Acta Numerica, vol.9, pp.215-365, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01328729

C. Kane, J. E. Marsden, and M. Ortiz, Symplectic-energy-momentum preserving variational integrators, J. Math. Phys, vol.40, issue.7, pp.3353-3371, 1999.

C. Kane, J. E. Marsden, M. Ortiz, and M. West, Variational integrators and the newmark algorithm for conservative and dissipative mechanical systems, Int. J. Numer. Methods Eng, vol.49, issue.10, pp.1295-1325, 2000.

C. Kane, E. A. Repetto, M. Ortiz, and J. E. Marsden, Finite element analysis of nonsmooth contact, Comput. Methods Appl. Mech. Eng, vol.180, issue.1, pp.1-26, 1999.

P. Krysl and L. Endres, Explicit Newmark/Verlet algorithm for time integration of the rotational dynamics of rigid bodies, Int. J. Numer. Methods Eng, vol.62, issue.15, pp.2154-2177, 2005.

S. Leyendecker, J. E. Marsden, and M. Ortiz, Variational integrators for constrained dynamical systems, ZAMM-Z. Angew. Math. Mech, vol.88, issue.9, pp.677-708, 2008.

C. Mariotti, A new leapfrog scheme for rotational motion in 3d, Int. J. Numer. Methods Eng, vol.107, issue.4, pp.273-289, 2016.

J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numerica, vol.10, pp.357-514, 2001.

G. R. Quispel and D. I. Mclaren, A new class of energy-preserving numerical integration methods, J. Phys. A Math. Theor, vol.41, issue.4, p.45206, 2008.

J. Salomon, A. A. Weiss, and B. Wohlmuth, Energy-conserving algorithms for a corotational formulation, SIAM J. Numer. Anal, vol.46, issue.4, pp.1842-1866, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00363422

J. Simo and J. Oliver, A new approach to the analysis and simulation of strain softening in solids. Fracture Damage Quasibrittle Struct, pp.25-39, 1994.

B. Wohlmuth, Variationally consistent discretization schemes and numerical algorithms for contact problems, Acta Numerica, vol.20, pp.569-734, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01382364