Foundations of Mechanics, 2nd edn, revised and enlarged. With the assistance of Tudor Ratiu and Richard Cushman, 1978. ,
Kirchhoff???s problem for nonlinearly elastic rods, Quarterly of Applied Mathematics, vol.32, issue.3, pp.221-240, 1974. ,
DOI : 10.1090/qam/667026
Nonlinear Problems in Elasticity, 1995. ,
DOI : 10.1007/978-1-4757-4147-6
On the parametrization of finite rotations in computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.3-4, pp.273-305, 1998. ,
DOI : 10.1016/S0045-7825(97)00158-8
Frame-indifferent beam finite elements based upon the geometrically exact beam theory, International Journal for Numerical Methods in Engineering, vol.48, issue.12, pp.1775-1788, 2002. ,
DOI : 10.1002/nme.487
Constrained dynamics of geometrically exact beams, Computational Mechanics, vol.31, issue.1-2, pp.49-59, 2003. ,
DOI : 10.1007/s00466-002-0392-1
Discrete Time Lagrangian Mechanics on Lie Groups,??with an Application to the Lagrange Top, Communications in Mathematical Physics, vol.204, issue.1, pp.147-188, 1999. ,
DOI : 10.1007/s002200050642
Discrete Lagrangian reduction, discrete Euler?Poincaré equations, and semidirect products, Letters in Mathematical Physics, vol.49, issue.1, pp.79-93, 1999. ,
DOI : 10.1023/A:1007654605901
Geometric invariance, Computational Mechanics, vol.29, issue.2, pp.163-169, 2002. ,
DOI : 10.1007/s00466-002-0329-8
Hamilton???Pontryagin Integrators on Lie Groups Part??I: Introduction and Structure-Preserving Properties, Foundations of Computational Mathematics, vol.57, issue.2, pp.197-219, 2009. ,
DOI : 10.1007/s10208-008-9030-4
Stochastic variational integrators, IMA Journal of Numerical Analysis, vol.29, issue.2, pp.421-443, 2008. ,
DOI : 10.1093/imanum/drn018
On the use of Lie group time integrators in multibody dynamics Special issue on Multi-disciplinary High-Performance Computational Multibody Dynamics, J. Comput. Nonlinear Dyn, vol.51, issue.3, p.031002104001370, 1115. ,
Lie group generalized-?? time integration of constrained flexible multibody systems, Mechanism and Machine Theory, vol.48, pp.1212-137, 2012. ,
DOI : 10.1016/j.mechmachtheory.2011.07.017
Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation, Proc. R. Soc. Lond. A 455, pp.1125-1147, 1999. ,
DOI : 10.1098/rspa.1999.0352
Some Applications of Semi-Discrete Variational Integrators to Classical Field Theories, Qualitative Theory of Dynamical Systems, vol.7, issue.1, pp.195-212, 2008. ,
DOI : 10.1007/s12346-008-0011-4
Multisymplectic Lie group variational integrator for a geometrically exact beam in, Communications in Nonlinear Science and Numerical Simulation, vol.19, issue.10, pp.3492-3512, 2014. ,
DOI : 10.1016/j.cnsns.2014.02.032
URL : https://hal.archives-ouvertes.fr/hal-01086681
Hamiltonian Formulations and Symmetries in Rod Mechanics, In: Mathematical Approaches to Biomolecular Structure and Dynamics, vol.82, pp.71-113, 1996. ,
DOI : 10.1007/978-1-4612-4066-2_6
Symmetry Reduced Dynamics of Charged Molecular Strands, Archive for Rational Mechanics and Analysis, vol.104, issue.2, pp.811-902, 2010. ,
DOI : 10.1007/s00205-010-0305-y
Nonsmooth Lagrangian Mechanics and Variational Collision Integrators, SIAM Journal on Applied Dynamical Systems, vol.2, issue.3, pp.381-416, 2003. ,
DOI : 10.1137/S1111111102406038
Variational principles for spin systems and the Kirchhoff rod, The Journal of Geometric Mechanics, vol.1, issue.4, pp.417-444, 2009. ,
DOI : 10.3934/jgm.2009.1.417
Reduced Variational Formulations in Free Boundary Continuum Mechanics, Journal of Nonlinear Science, vol.104, issue.6, pp.463-497, 2012. ,
DOI : 10.1007/s00332-012-9143-4
URL : https://hal.archives-ouvertes.fr/hal-01114752
Time integration and discrete Hamiltonian systems, Journal of Nonlinear Science, vol.115, issue.5, pp.449-467, 1996. ,
DOI : 10.1007/BF02440162
Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations, 2006. ,
Computational aspects of vector-like parametrization of three-dimensional finite rotations, International Journal for Numerical Methods in Engineering, vol.34, issue.21, pp.3653-3673, 1995. ,
DOI : 10.1002/nme.1620382107
Finite rotations in dynamics of beams and implicit time-stepping schemes, International Journal for Numerical Methods in Engineering, vol.15, issue.5, pp.781-814, 1998. ,
DOI : 10.1002/(SICI)1097-0207(19980315)41:5<781::AID-NME308>3.0.CO;2-9
Lie-group methods. Acta Num, pp.215-365, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-01328729
Interpolation of rotational variables in nonlinear dynamics of 3D beams, International Journal for Numerical Methods in Engineering, vol.15, issue.7, pp.1193-1222, 1998. ,
DOI : 10.1002/(SICI)1097-0207(19981215)43:7<1193::AID-NME463>3.0.CO;2-P
Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics, Computer Methods in Applied Mechanics and Engineering, vol.171, issue.1-2, pp.141-171, 1999. ,
DOI : 10.1016/S0045-7825(98)00249-7
Problems associated with the use of Cayley transform and tangent scaling for conserving energy and momenta in the Reissner-Simo beam theory, Communications in Numerical Methods in Engineering, vol.49, issue.10, pp.711-720, 2002. ,
DOI : 10.1002/cnm.531
A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria, International Journal for Numerical Methods in Engineering, vol.167, issue.2, pp.31-60, 2010. ,
DOI : 10.1002/nme.2950
Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems, International Journal for Numerical Methods in Engineering, vol.76, issue.10, pp.1295-1325, 2000. ,
DOI : 10.1002/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W
Discrete Geometric Optimal Control on Lie Groups, IEEE Transactions on Robotics, vol.27, issue.4, pp.641-655, 2011. ,
DOI : 10.1109/TRO.2011.2139130
Geometric discretization of nonholonomic systems with symmetries, Discrete Contin. Dyn. Syst. Ser. S, vol.3, issue.1, pp.61-84, 2010. ,
Multi-body dynamics simulation of geometrically exact Cosserat rods, Multibody System Dynamics, vol.198, issue.3, pp.285-312, 2011. ,
DOI : 10.1007/s11044-010-9223-x
Numerical aspects in the dynamic simulation of geometrically exact rods, Applied Numerical Mathematics, vol.62, issue.10, pp.1411-1427, 2012. ,
DOI : 10.1016/j.apnum.2012.06.011
Dynamics of a 3D elastic string pendulum, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009. ,
DOI : 10.1109/CDC.2009.5399611
Computational geometric mechanics and control of rigid bodies, 2008. ,
Asynchronous Variational Integrators, Archive for Rational Mechanics and Analysis, vol.167, issue.2, pp.85-146, 2003. ,
DOI : 10.1007/s00205-002-0212-y
Variational time integrators, International Journal for Numerical Methods in Engineering, vol.60, issue.1, pp.153-212, 2004. ,
DOI : 10.1002/nme.958
An overview of variational integrators Finite Element Methods: 1970's and Beyond, CIMNE, pp.98-115, 2004. ,
Objective energy???momentum conserving integration for the constrained dynamics of geometrically exact beams, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.19-22, pp.2313-2333, 2006. ,
DOI : 10.1016/j.cma.2005.05.002
The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part??III: Flexible multibody dynamics, Multibody System Dynamics, vol.37, issue.4, pp.45-72, 2008. ,
DOI : 10.1007/s11044-007-9056-4
Variational integrators for constrained dynamical systems, ZAMM, vol.60, issue.10, pp.677-708, 2008. ,
DOI : 10.1002/zamm.200700173
A Variational Approach to Multirate Integration for Constrained Systems, Thematic Conference: Multibody Dynamics: Computational Methods and Applications, pp.4-7, 2011. ,
DOI : 10.1007/978-94-007-5404-1_5
Discrete mechanics and optimal control for constrained systems, Optimal Control Applications and Methods, vol.88, issue.6, pp.505-528, 2010. ,
DOI : 10.1002/oca.912
Mathematical Foundations of Elasticity, Journal of Applied Mechanics, vol.51, issue.4, 1994. ,
DOI : 10.1115/1.3167757
Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs, Communications in Mathematical Physics, vol.199, issue.2, pp.351-395, 1998. ,
DOI : 10.1007/s002200050505
Discrete Euler-Poincar?? and Lie-Poisson equations, Nonlinearity, vol.12, issue.6, pp.1647-1662, 1999. ,
DOI : 10.1088/0951-7715/12/6/314
Introduction to Mechanics and Symmetry, 1999. ,
Discrete mechanics and variational integrators, Acta Numerica 2001, vol.10, pp.357-514, 2001. ,
DOI : 10.1017/S096249290100006X
Discrete versions of some classical integrable systems and factorization of matrix polynomials, Communications in Mathematical Physics, vol.42, issue.4, pp.217-243, 1991. ,
DOI : 10.1007/BF02352494
Discrete mechanics and optimal control: An analysis, ESAIM: Control, Optimisation and Calculus of Variations, vol.17, issue.2, pp.322-352, 2011. ,
DOI : 10.1051/cocv/2010012
On one-dimensional finite-strain beam theory: The plane problem, Zeitschrift f??r angewandte Mathematik und Physik ZAMP, vol.23, issue.5, pp.795-804, 1972. ,
DOI : 10.1007/BF01602645
On One-Dimensional Large-Displacement Finite-Strain Beam Theory, Studies in Applied Mathematics, vol.39, issue.2, pp.87-95, 1973. ,
DOI : 10.1002/sapm197352287
An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics, International Journal for Numerical Methods in Engineering, vol.190, issue.12, pp.1683-1716, 2002. ,
DOI : 10.1002/nme.486
The interpolation of rotations and its application to finite element models of geometrically exact rods, Computational Mechanics, vol.34, issue.2, pp.121-133, 2004. ,
DOI : 10.1007/s00466-004-0559-z
Dynamics of Multibody Systems, 1998. ,
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory, Journal of Mechanical Design, vol.123, issue.4, pp.606-613, 2001. ,
DOI : 10.1115/1.1410100
A finite strain beam formulation. The three-dimensional dynamic problem. Part I, Computer Methods in Applied Mechanics and Engineering, vol.49, issue.1, pp.79-116, 1985. ,
DOI : 10.1016/0045-7825(85)90050-7
The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates, Archive for Rational Mechanics and Analysis, vol.104, issue.2, pp.125-183, 1988. ,
DOI : 10.1007/BF00251673
A three-dimensional finite-strain rod model. part II: Computational aspects, Computer Methods in Applied Mechanics and Engineering, vol.58, issue.1, pp.55-70, 1986. ,
DOI : 10.1016/0045-7825(86)90079-4
On the dynamics in space of rods undergoing large motions ??? A geometrically exact approach, Computer Methods in Applied Mechanics and Engineering, vol.66, issue.2, pp.125-161, 1988. ,
DOI : 10.1016/0045-7825(88)90073-4
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging, Multiscale Modeling & Simulation, vol.8, issue.4, pp.1269-1324, 2010. ,
DOI : 10.1137/090771648