V. I. Arnold, Mathematical methods in classical mechanics, 1988.

J. Ayers, Underwater walking, Arthropod Structure & Development, vol.33, issue.3, pp.347-360, 2004.
DOI : 10.1016/j.asd.2004.06.001

D. S. Barette, M. S. Triantafyllou, D. K. Yue, M. A. Grosenbaugh, and M. J. Wolfgang, Drag reduction in fish-like locomotion, Journal of Fluid Mechanics, vol.392, pp.183-212, 1999.
DOI : 10.1017/S0022112099005455

G. K. Batchelor, An Introduction To Fluid Dynamics, 1967.
DOI : 10.1017/CBO9780511800955

R. W. Blake, Fish locomotion, 1991.

G. Bonnet, Méthode des équations integrales appliquée à la mécanique, Institu National polytechnique de Grenoble, 1988.

F. Boyer, Contribution à la modélisation et à la commande dynamique des robots flexibles, 1994.

F. Boyer and P. Coiffet, Generalization of Newton-Euler model for flexible manipulators, Journal of Robotic Systems, vol.7, issue.1, pp.11-24, 1996.
DOI : 10.1002/(SICI)1097-4563(199601)13:1<11::AID-ROB2>3.0.CO;2-Y

F. Boyer and W. Khalil, An Efficient Calculation of Flexible Manipulator Inverse Dynamics, The International Journal of Robotics Research, vol.17, issue.3, pp.282-293, 1998.
DOI : 10.1177/027836499801700305

URL : https://hal.archives-ouvertes.fr/hal-00629447

F. Boyer, M. Porez, and W. Khalil, Macro-continuous computed torque algorithm for a three-dimensional eel-like robot, IEEE Transactions on Robotics, vol.22, issue.4, pp.763-775, 2006.
DOI : 10.1109/TRO.2006.875492

URL : https://hal.archives-ouvertes.fr/hal-00630750

F. Boyer, M. Porez, and A. Leroyer, Poincaré-cosserat equations for lighthill threedimensional dynamic model of a self propolled eel devoted to robotics. Soumis, rapport interne de l'Ecole des Mines de Nantes no. : 07/8/Auto, disponible en ligne, 2007.

F. Boyer, M. Porez, A. Leroyer, and M. Visonneau, Fast dynamics of an eel-like robot , comparisons with navier-stokes simulations. Soumis, rapport interne de l'Ecole des Mines de Nantes no, 2007.

F. Boyer and D. Primault, Finite element of slender beams in finite transformations: a geometrically exact approach, International Journal for Numerical Methods in Engineering, vol.59, issue.5, pp.669-702, 2004.
DOI : 10.1002/nme.879

URL : https://hal.archives-ouvertes.fr/hal-00630745

F. Boyer and D. Primault, The Poincar??-Chetayev equations and flexible multibody systems, Journal of Applied Mathematics and Mechanics, vol.69, issue.6, pp.925-942, 2005.
DOI : 10.1016/j.jappmathmech.2005.11.015

C. M. Breder, The locomotion fishes, Zoologica, vol.4, pp.159-256, 1926.

J. Canavin and P. W. Likins, Floating reference frames for flexible spacecraft, AIAA 15th. Aerospace Sciences Meeting, pp.66-77, 1977.
DOI : 10.2514/3.57256

J. Carling, T. L. Williams, and G. Bowtell, Self-propelled anguilliform swimming : simultaneous solution of the two-dimensional navier-stokes equations and newton's laws of motion, J. Exp. Bio, vol.201, pp.3243-3166, 1998.

J. Cheng and R. Blinckhan, Bending Moment Distribution along Swimming Fish, Journal of Theoretical Biology, vol.168, issue.3, pp.337-348, 1994.
DOI : 10.1006/jtbi.1994.1114

J. Cheng and G. L. Chahine, Computational hydrodynamics of animal swimming: boundary element method and three-dimensional vortex wake structure, Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology, vol.131, issue.1, pp.51-60, 2001.
DOI : 10.1016/S1095-6433(01)00464-0

J. Cheng, T. J. Pedley, and J. D. Altringham, A continuous dynamic beam model for swimming fish, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.353, issue.1371, pp.981-997, 1998.
DOI : 10.1098/rstb.1998.0262

G. S. Chirikjian and J. W. Burdick, An obstacle avoidance algorithm for hyper-redundant manipulators, Proceedings., IEEE International Conference on Robotics and Automation, pp.14-17, 1990.
DOI : 10.1109/ROBOT.1990.126052

J. Coirier, Mécanique des Milieux continus (seconde edition) Dunod, 2001.

J. E. Colgate and K. M. Lynch, Mechanics and Control of Swimming: A Review, IEEE Journal of Oceanic Engineering, vol.29, issue.3
DOI : 10.1109/JOE.2004.833208

E. Cosserat and F. Cosserat, Théorie des corps déformables, 1909.

G. H. Cottet and P. D. Koumoutsakos, Vortex Methods : Theory and Practice, 2000.
DOI : 10.1017/CBO9780511526442

K. D. Aout and P. Aerts, A kinematic comparison of forward and backward swimming in the eel anguilla anguilla, J. Exp. Biol, vol.202, pp.1511-1521, 1999.

G. Dhatt, G. Touzot, and E. Lefrançois, Méthode des Eléments Finis, Hermes Science, 2005.

T. Doi, R. Hodoshima, Y. Fukuda, S. Hirose, T. Okamoto et al., Development of quadruped walking robot titan xi for steep slopes -slope map generation and map information application, J. of Robotics and Mechatronics, vol.18, pp.318-324, 2006.

M. El-rafei, M. Alamir, G. Hafidi, N. Marchand, M. Porez et al., Motion control of three-dimensional eel-like robot, IEEE International Conference on Robotics and Automation, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00199433

T. E. Faber, Fluid Dynamics for Scientists, 1995.

D. J. Farnell, T. David, and D. C. Barton, Numerical model of self-propulsion in a fluid, Journal of The Royal Society Interface, vol.207, issue.11, pp.79-88, 2005.
DOI : 10.1242/jeb.00968

R. Featherstone, The Calculation of Robot Dynamics Using Articulated-Body Inertias, The International Journal of Robotics Research, vol.93, issue.2, pp.13-30, 1983.
DOI : 10.1177/027836498300200102

R. Featherstone and D. Orin, Robot dynamics: equations and algorithms, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), pp.826-834, 2000.
DOI : 10.1109/ROBOT.2000.844153

URL : http://axiom.anu.edu.au/~roy/papers/icra00.pdf

D. François, A. Pineau, and A. Zaoui, Comportement mécanique des matériaux élasticité et plasticité, 1991.

A. Friedman, G. Zilmen, and T. Miloh, Dynamics of body faling in waves, 18th International Workshop o Water Waves & Floating Bodies, 2003.

G. Gallot, O. Ibrahim, and W. Khalil, Dynamic Modeling and simulation of a 3-D Hybrid structure Eel-Like Robot, Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007.
DOI : 10.1109/ROBOT.2007.363194

S. F. Galls and O. K. Rediniotis, Computational Simulation of the Autonomous Navigation of a Biomimetic Underwater Vehicle, AIAA Journal, vol.41, issue.4, pp.605-611, 2003.
DOI : 10.2514/2.2014

A. R. Galper, T. Miloh, and M. Spector, Hydrodynamic loads on a slender cylinder moving unsteadily in a 3-D non-uniform flow field, Applied Ocean Research, vol.18, issue.1, pp.29-36, 1996.
DOI : 10.1016/0141-1187(96)00018-1

P. Germain and P. Muller, Introduction à la Mécanique des Milieux Continus (seconde édition), 1995.

K. Gieck and R. Gieck, Formulaire technique, Gieck, 1997.

G. B. Gillis, Environmental effects on undulatory locomotion in the american eel anguilla rostata : kinematics in water and on land, J. Exp. Bio, vol.201, pp.949-961, 1998.

H. Glauert, The Element of Aerofoil and Airscrew Theory (second edition), 1947.

J. Gray, Studies in animal locomotion. i. the movement of fish with special reference to the eel, J. Exp. Bio, vol.10, pp.88-104, 1933.

J. Gray, Studies in animal locomotion. vi. the propulsive powers of the dolphin, J. Exp. Bio, vol.13, pp.192-199, 1936.

M. W. Hannan and I. D. Walker, Kinematics and the Implementation of an Elephant's Trunk Manipulator and Other Continuum Style Robots, Journal of Robotic Systems, vol.3, issue.2, pp.45-63, 2003.
DOI : 10.1002/rob.10070

J. L. Hess and A. M. Smith, Calculation of potential flow about arbitrary bodies, Progress in Aeronautical Sciences, pp.1-138, 1966.
DOI : 10.1016/0376-0421(67)90003-6

S. J. Hill, Large amplitude fish swimming, 1998.

. Hirose, Biologically inspired robots : snake-like locomotors and manipulators, 1993.
DOI : 10.1109/robio.2004.1521742

S. F. Hoerner, Fluid Dynamics Drag. Hoerner Fluid Dynamics, 1965.

D. Hristu-varsakelis and W. S. Levine, Handbook of Networked and Embedded Control Systems, 2005.
DOI : 10.1007/b137198

A. J. Ijspeert, A. Crespi, and J. Cabelguen, Simulation and robotics studies f salamander locomotion. applying neurobiological principles to the contro of locomotion in robots, Neuroinformatics, vol.5, pp.171-196, 2005.
DOI : 10.1385/ni:3:3:171

URL : http://infoscience.epfl.ch/record/58531

C. E. Jordan, A model of rapid-start swimming at intermediate reynolds number : undulatory locomotion in the chaetognth sagitta elegans, J. Exp. Bio, vol.163, pp.119-137, 1991.

E. Kanso, J. E. Marsden, C. W. Rowley, and J. Melli-huber, Locomotion of Articulated Bodies in a Perfect Fluid, Journal of Nonlinear Science, vol.15, issue.4, pp.255-289, 2005.
DOI : 10.1007/s00332-004-0650-9

I. Kassim, L. Phee, W. S. Ng, F. Gong, P. Dario et al., Locomotion techniques for robotic colonoscopy, IEEE Engineering in Medicine and Biology Magazine, vol.25, issue.3, pp.49-56, 2006.
DOI : 10.1109/MEMB.2006.1636351

J. Katz and A. Plotkin, Low-Speed Aerodynamics, 2001.
DOI : 10.1017/CBO9780511810329

S. Katzen, The Quintessential PIC Microcontroller, 2005.
DOI : 10.1007/978-1-4471-3704-7

D. K. Kelly and R. M. Murray, Geometric phases and robotic locomotion, Journal of Robotic Systems, vol.104, issue.5, pp.417-431, 1995.
DOI : 10.1002/rob.4620120607

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.4566

W. Khalil and E. Dombre, Modeling, Identification and Control of Robots. Penton- Sciences, 2002.

W. Khalil, G. Gallot, and F. Boyer, Dynamic Modeling and Simulation of a 3-D Serial Eel-Like Robot, IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), vol.37, issue.6, 2006.
DOI : 10.1109/TSMCC.2007.905831

URL : https://hal.archives-ouvertes.fr/hal-00630752

G. Kirchhoff, Ueber die bewegung eines rotationskörpers in einer flüssigkeit, Journal für die reine und angewandte Mathematik, pp.237-262, 1869.

J. Kutta, Auftriebskräfte in strömenden flüssigkeiten, Illustrierte Aueronautische Mitteilungen, vol.6, pp.133-135, 1902.

A. Leroyer, Etude du couplage écoulement/mouvement pour les corps solides ou à déformation imposée par résolution des équations de Navier-Stokes. Contributon à la modélisation numérique de la cavitation, 2004.

A. Leroyer and M. Visonneau, Numerical methods for RANSE simulations of a self-propelled fish-like body, Journal of Fluids and Structures, vol.20, issue.7, pp.975-991, 2005.
DOI : 10.1016/j.jfluidstructs.2005.05.007

URL : https://hal.archives-ouvertes.fr/hal-00699458

E. V. Lewis, Principles of Naval Architecture. Volume III. Motions in Waves and Controllability. The society of Naval Architects & Marine Engineers, 1989.

R. I. Lewis, Vortex Element Methods for Fluid Dynamic Analysis of Engineerin Systems, 1991.

A. Lichnerowicz, Eléments de calcul tensoriel, Jacques Gabay, 1948.

Q. Liu and K. Kawachi, A Numerical Study of Undulatory Swimming, Journal of Computational Physics, vol.155, issue.2, pp.223-247, 1999.
DOI : 10.1006/jcph.1999.6341

J. Y. Luh, M. W. Walker, and R. C. Paul, On-Line Computational Scheme for Mechanical Manipulators, Journal of Dynamic Systems, Measurement, and Control, vol.102, issue.2, pp.69-76, 1980.
DOI : 10.1115/1.3149599

M. A. Maciver, E. Fontaine, and J. W. Burdick, Designing Future Underwater Vehicles: Principles and Mechanisms of the Weakly Electric Fish, IEEE Journal of Oceanic Engineering, vol.29, issue.3, pp.651-659, 2004.
DOI : 10.1109/JOE.2004.833210

L. E. Malvern, Introduction to the mechanics of a continuous medium, 1969.

J. E. Marsden and T. J. Hughes, Mathematical Foundations of Elasticity, Journal of Applied Mechanics, vol.51, issue.4, 1994.
DOI : 10.1115/1.3167757

J. E. Marsden and T. S. Ratiu, Introduction to mechanics and symmetry, scnd, 1999.
DOI : 10.1007/978-1-4612-2682-6

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.5772

K. A. Mcisaac and J. P. Ostrowski, A geometric approach to anguilliform locomotion modelling of an underwater eel robot, IEEE Int. Conf. Robotics and Automation, 1999.

J. B. Melli, C. W. Rowley, and D. S. Rufat, Motion Planning for an Articulated Body in a Perfect Planar Fluid, SIAM Journal on Applied Dynamical Systems, vol.5, issue.4, pp.650-669, 2006.
DOI : 10.1137/060649884

A. Menciassi, S. Gorini, G. Pernorio, and P. Dario, A SMA actuated artificial earthworm, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004, pp.3282-3287, 2004.
DOI : 10.1109/ROBOT.2004.1308760

J. P. Merlet, Parallel Robots, 2000.
DOI : 10.1007/978-94-010-9587-7

URL : https://hal.archives-ouvertes.fr/lirmm-00127856

R. E. Meyer, Introduction to Mathematical Fluid Dynamics, 1971.

L. M. Milne-thomson, Theoretical Hydrodynamics, 1968.

J. R. Morison, The Force Exerted by Surface Waves on Piles, Journal of Petroleum Technology, vol.2, issue.05, pp.149-154, 1950.
DOI : 10.2118/950149-G

M. M. Munk, The aerodynamic forces on airship hulls, National Advisory Commitee for Aeronautics, vol.184, 1924.

U. K. Müller, B. L. Van-den-heuvel, E. J. Stamhuis, and J. J. Videler, Fish foot prints : morphology and energetics of the wake behind a continuously swimming mullet (chelon labrosus risso), J. of Exp. Biol, vol.200, pp.2893-2906, 1997.

U. K. Müller, J. Smit, E. J. Stanhuis, and J. J. Videler, How the body contibutes to the wake in undulatory fish swimming : flow fields of a swimming eel (anguilla anguilla), J. Exp. Bio, vol.204, pp.2751-2762, 2001.

J. N. Newman, The force on a slender fish-like body, Journal of Fluid Mechanics, vol.9, issue.04, pp.689-702, 1973.
DOI : 10.1017/S0022112073002429

J. P. Ostrowski and J. W. Burdick, The Geometric Mechanics of Undulatory Robotic Locomotion, The International Journal of Robotics Research, vol.17, issue.7, pp.683-701683, 1998.
DOI : 10.1177/027836499801700701

D. Paret, Réseaux multiplexés pour systèmes embarqués : Can, Lin, FlexRay, Safeby-Wire, 2005.

T. J. Pedley and S. J. Hill, Large-amplitude undulatory fish swimming : fluid mechanics coupled to internal mechnanics, J. Exp. Bio, vol.202, pp.3431-3438, 1999.

H. Poincaré, Sur une forme nouvelle des équations de la mécanique Compte rendu de l'académie des sciences de Paris, pp.369-371, 1901.

J. F. Pommaret, Partial differential Equations and group theory, 1994.
DOI : 10.1007/978-94-017-2539-2

W. Regan, F. Van-breugel, and H. Lipson, Towards evolvable hovering flight on a physical ornithopter, In Alife X, 2006.

E. Reissner, 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

M. J. Ringuette, Vortex formation and drag on low aspect ratio, normal flat plates, 2004.

F. Ruffier and N. Franceschini, Optic flow regulation: the key to aircraft automatic guidance, Robotics and Autonomous Systems, vol.50, issue.4, pp.177-194, 2005.
DOI : 10.1016/j.robot.2004.09.016

T. Sarpkaya, In - Line And Transverse Forces, On Cylinders In Oscillatory Flow At High Reynolds Numbers., Offshore Technology Conference, pp.200-216, 1977.
DOI : 10.4043/2533-MS

T. Sarpkaya, Force on a circular cylinder in viscous oscillatory flow at low keulegancarpenter numbers, J. of fluid mechanics, vol.133, pp.265-285, 1986.

C. Schuil, M. Valente, J. Werfel, and R. Nagpal, Collective construction using lego robots, Robot Exhibition, National Conference on Artificial Intelligence (AAAI), 2006.

M. Sfakiotakis, D. M. Lane, and J. B. Davies, Review of fish swimming modes for aquatic locomotion, IEEE Journal of Oceanic Engineering, vol.24, issue.2, pp.237-252, 1999.
DOI : 10.1109/48.757275

J. C. Simo, A finite strain beam formulation. The three-dimensional dynamic problem. Part I, Computer Methods in Applied Mechanics and Engineering, vol.49, issue.1, pp.267-304, 1985.
DOI : 10.1016/0045-7825(85)90050-7

J. C. Simo and L. Vu-quoc, On the Dynamics of Flexible Beams Under Large Overall Motions???The Plane Case: Part I, Journal of Applied Mechanics, vol.53, issue.4, pp.849-854, 1986.
DOI : 10.1115/1.3171870

J. C. Simo and L. Vu-quoc, On the Dynamics of Flexible Beams Under Large Overall Motions???The Plane Case: Part II, Journal of Applied Mechanics, vol.53, issue.4, pp.855-863, 1986.
DOI : 10.1115/1.3171871

J. C. Simo and L. Vu-quoc, A three-dimensional finite-strain rod model. part II: Computational aspects, Computer Methods in Applied Mechanics and Engineering, vol.58, issue.1, pp.79-116, 1986.
DOI : 10.1016/0045-7825(86)90079-4

J. C. Simo and L. Vu-quoc, 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

J. A. Sparenberg, Survey of the mathematical theory of fish locomotion, Journal of Engineering Mathematics, vol.44, issue.4, pp.395-448, 2002.
DOI : 10.1023/A:1021256500244

G. I. Taylor, Analysis of the Swimming of Long and Narrow Animals, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.214, issue.1117, pp.158-183, 1952.
DOI : 10.1098/rspa.1952.0159

A. H. Techet and . M. Hydrodynamics, Course of Hydrodynamics for Ocean Engineers, 2005.

M. S. Triantafyllou and G. S. Triantafyllou, An Efficient Swimming Machine, Scientific American, vol.272, issue.3, pp.64-70, 1995.
DOI : 10.1038/scientificamerican0395-64

M. S. Triantafyllou, G. S. Triantafyllou, and R. Gopalkrishnan, Optimal Thrust Development in Oscillating Foils with Application to Fish Propulsion, Journal of Fluids and Structures, vol.7, issue.2, pp.205-224, 1993.
DOI : 10.1006/jfls.1993.1012

M. S. Triantafyllou, G. S. Triantafyllou, and D. K. Yue, Hydrodynamics of Fishlike Swimming, Annual Review of Fluid Mechanics, vol.32, issue.1, pp.33-53, 2000.
DOI : 10.1146/annurev.fluid.32.1.33

D. P. Tsakiris, A. Menciassi, M. Sfakiotakis, G. L. Spina, and P. Dario, Undulatory locomotion of polychaete annelids : mechanics, neural control and robotic prototypes, Annual Computational Neuroscience Meeting, 2004.

E. D. Tytell and G. V. Lauder, The hydrodynamics of eel swimming: I. Wake structure, Journal of Experimental Biology, vol.207, issue.11, pp.1825-1841, 2004.
DOI : 10.1242/jeb.00968

V. Van-ginneken, E. Antonissen, U. K. Müller, R. Booms, E. Eding et al., Eel migration to the Sargasso: remarkably high swimming efficiency and low energy costs, Journal of Experimental Biology, vol.208, issue.7, pp.1329-1335, 2005.
DOI : 10.1242/jeb.01524

J. J. Videler, Fish Swimming, Fish and Fisheries Series, vol.10, 1993.
DOI : 10.1007/978-94-011-1580-3

J. J. Videler, U. K. Müller, and E. J. Stamhuis, Aquatic vertebrate locomotion : wakes from body waves, J. Exp. Biol, vol.202, pp.3423-3430, 1999.

L. Vu-quoc, On the algebra of two point tensors and their applications. in ZAMM, Z. angew. Math. Mech, vol.76, issue.9, pp.540-541, 1996.

D. Weihs, Hydrodynamical analysis fish turning manoeuvres. National Advisory Commitee for Aeronautics, pp.59-72, 1972.

M. J. Wolfgang, Hydrodynamics of flexible-body swimming motions, 1999.

T. Wu, Swimming of a waving plate, Journal of Fluid Mechanics, vol.64, issue.03, pp.321-355, 1961.
DOI : 10.1017/S0022112060001110

T. Wu, Hydromechanics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid, Journal of Fluid Mechanics, vol.209, issue.02, pp.337-355, 1971.
DOI : 10.1146/annurev.fl.01.010169.002213

H. Yamada, S. Chigisaki, M. Mori, K. Takita, K. Ogami et al., Development of amphibious snake-like robot acm-r5, the proceding of 36th international symposium on robotics ISR2005 Japan, 2005.

J. Yan, S. A. Avadhanula, J. Birch, M. H. Dickinson, M. Sitti et al., Wing transmission for a micromechanical flying insect, Journal of Micromechatronics, vol.1, issue.3, pp.221-258, 2002.
DOI : 10.1163/156856301760132123

J. Yuh, Design and control of autonomous underwater robots : a survey, Autonomous Robots, vol.8, issue.1, pp.7-24, 2000.
DOI : 10.1023/A:1008984701078

Q. Zhu, M. J. Wolfgang, D. K. Yue, and M. S. Triantafyllou, Three-dmensional flow structures and vorticity control in fish-like swimming, J. Fluid Mech, vol.468, pp.1-28, 2002.