References
- Alouges, F., DeSimone, A. and Lefebvre, A. (2008). Optimal Strokes for low Reynolds number swimmers: An example, Journal of Nonlinear Science 18: 27-302.
- Becker, L.E, Koehler, S.A. and Stone, H.A. (2003). On self-propulsion of micro-machines at low Reynolds number: Purcell’s three-link swimmer, Journal of FluidMechanics 490: 15-35.
- Belter, D. and Skrzypczy´nski, P (2010). A biologically inspired approach to feasible gait learning for a hexapod robot, InternationalJournal of Applied Mathematics and ComputerScience 20(1): 69-84, DOI: 10.2478/v10006-010-0005-7.
- Childress, S. (1981). Mechanics of Swimming and Flying, Cambridge University Press, Cambridge.
- Dal Maso, Gi., DeSimone, A. and Morandotti, M. (2011). An existence and uniqueness result for the motion of self-propelled micro-swimmers, SIAM Journal of MathematicalAnalysis 43: 1345-1368.
- Fukuda, T., Kawamoto, A., Arai, F. and Matsuura, H. (1995). Steering mechanism and swimming experiment of micro mobile robot in water, Proceedings of Micro Electro MechanicalSystems (MEMS’95), Amsterdam, The Netherlands, pp. 300-305.
- Fauci, L. and Peskin, C.S. (1988). A computational model of aquatic animal locomotion, Journal of ComputationalPhysics 77: 85-108.
- Fauci, L. (1993). Computational modeling of the swimming of biflagellated algal cells, Contemporary Mathematics 141: 91-102.
- Galdi, G.P. (1999). On the steady self-propelled motion of a body in a viscous incompressible fluid, Archive for RationalMechanics and Analysis 1448: 53-88.
- Galdi, G.P. (2002). On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, in S. Friedlander and D. Serre (Eds.), Handbook of MathematicalFluid Mechanics, Elsevier Science, Amsterdam, pp. 653-791.
- Gray, J. (1932). Study in animal locomotion IV: The propulsive power of the dolphin, Journal of Experimental Biology 10: 192-199.
- Gray, J. and Hancock, G.J. (1955). The propulsion of sea-urchin spermatozoa, Journal of Experimental Biology 32: 802.
- Guo, S. (2002). Afin type of micro-robot in pipe, Proceedingsof the 2002 International Symposium on Micromechatronicsand Human Science (MHS 2002), Ngoya, Japan, pp. 93-98.
- Gurtin, M.E. (1981). An Introduction to Continuum Mechanics, Academic Press, New York, NY.
- Hawthorne,M.F., Zink, J.I., Skelton, J.M., Bayer,M.J., Liu, Ch., Livshits, E., Baer, R. and Neuhauser, D. (2004). Electrical or photocontrol of rotary motion of a metallacarborane, Science 303: 1849.
- Happel, V. and Brenner, H. (1965). Low Reynolds Number Hydrodynamics, Prentice Hall, Upper Saddle River, NJ.
- Hirose, S. (1993). Biologically Inspired Robots: Snake-likeLocomotors and Manipulators, Oxford University Press, Oxford.
- Kanso. E., Marsden, J.E., Rowley, C.W. and Melli-Huber, J. (2005). Locomotion of articulated bodies in a perfect fluid, Journal of Nonlinear Science 15: 255-289.
- Khapalov, A.Y. (1999). Approximate controllability properties of the semilinear heat equation with lumped controls, InternationalJournal of Applied Mathematics and ComputerScience 9(4): 751-765.
- Khapalov, A.Y. (2005). The well-posedness of a model of an apparatus swimming in the 2-D Stokes fluid, Technical Report 2005-5, Washington State University, Department of Mathematics, http://www.math.wsu.edu/TRS/2005-5.pdf.
- Khapalov, A.Y. and Eubanks, S. (2009). The wellposedness of a 2-D swimming model governed in the nonstationary Stokes fluid by multiplicative controls, Applicable Analysis88: 1763-1783, DOI:10.1080/00036810903401222.
- Khapalov, A.Y. (2010). Controllability of Partial DifferentialEquations Governed by Multiplicative Controls, Lecture Notes in Mathematics Series, Vol. 1995, Springer-Verlag, Berlin/Heidelberg.
- Khapalov, A.Y. and Trinh, G. (2013). Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid, Discrete and Continuous DynamicalSystems Series A 33: 1513-1544.
- Khapalov, A.Y. (2013). Micro motions of a swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, arXiv: 1205.1088 [math.AP], (preprint).
- Koiller, J., Ehlers, F. and Montgomery, R. (1996). Problems and progress in microswimming, Journal of Nonlinear Science6: 507-541.
- Ladyzhenskaya, O.A. (1963). The Mathematical Theory of ViscousIncompressible Flow, Cordon and Breach, New York, NY.
- Lighthill, M.J. (1975). Mathematics of Biofluid Dynamics, Society for Industrial and Applied Mathematics, Philadelphia, PA.
- Mason, R. and Burdick, J.W. (2000). Experiments in carangiform robotic fish locomotion, Proceedings of theIEEE International Conference on Robotics and Automation,San Francisco, CA, USA, pp. 428-435.
- McIsaac, K.A. and Ostrowski, J.P. (2000). Motion planning for dynamic eel-like robots, Proceedings of the IEEE InternationalConference on Robotics and Automation, San Francisco,CA, USA, pp. 1695-1700.
- Martinez, S. and Cortes, J. (2001). Geometric control of robotic locomotion systems, Proceedings of the 10th Fall Workshopon Geometry and Physics, Miraflores de la Sierra,Spain, Vol. 4, pp. 183-198.
- Morgansen, K.A., Duindam, V., Mason, R.J., Burdick, J.W. and Murray, R.M. (2001). Nonlinear control methods for planar carangiform robot fish locomotion, Proceedings ofthe IEEE International Conference on Robotics and Automation,Seoul, Korea, pp. 427-434.
- Peskin, C.S. (1977). Numerical analysis of blood flow in the heart, Journal of Computational Physics 25: 220-252.
- Peskin, C.S. and McQueen, D.M. (1994). A general method for the computer simulation of biological systems interacting with fluids, SEB Symposium on Biological Fluid Dynamics,Leeds, UK.
- San Martin, J., Takashi, T. and Tucsnak, M. (2007). A control theoretic approach to the swimming of microscopic organisms, Quarterly Applied Mathematics 65: 405-424.
- San Martin, J., Scheid, J.-F., Takashi, T. and Tucsnak, M. (2008). An initial and boundary value problem modeling of fish-like swimming, Archive of Rational Mechanics andAnalysis 188: 429-455.
- Shapere, A. and Wilczeck, F. (1989). Geometry of self-propulsion at low Reynolds number, Journal of FluidMechanics 198: 557-585.
- Sigalotti, M. and Vivalda, J.-C. (2009). Controllability properties of a class of systems modeling swimming microscopic organisms, ESAIM: Control, Optimisationand Calculus of Variations 16: 1053-1076.
- Taylor, G.I. (1951). Analysis of the swimming of microscopic organisms, Proceeding of the Royal Society of London A209: 447-461.
- Taylor, G.I. (1952). Analysis of the swimming of long and narrow animals, Proceedings of the Royal Society of LondonA 214(1117): 158-183.
- Temam, R. (1984). Navier-Stokes Equations, North-Holland, Amsterdam.
- Trintafyllou, M.S., Trintafyllou, G.S. and Yue, D.K.P. (2000). Hydrodynamics of fishlike swimming, Annual Review ofFluid Mechanics 32: 33-53.
- Tytell, E.D., Hsu, C.-Y, Williams, T.L., Cohen, A.H. and Fauci, L.J. (2010). Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming, Proceedings of the NationalAcademy Sciences, USA 107: 19832-19837.
- Wu, T.Y. (1971). Hydrodynamics of swimming fish and cetaceans, Advances in Applied Mathematics 11: 1-63.