Free Access
Issue
ESAIM: COCV
Volume 16, Number 4, October-December 2010
Page(s) 1053 - 1076
DOI https://doi.org/10.1051/cocv/2009034
Published online 11 August 2009
  1. A.A. Agrachev and Y.L. Sachkov, Control theory from the geometric viewpoint, Encyclopaedia of Mathematical Sciences 87, Control Theory and Optimization II. Springer-Verlag, Berlin (2004). [Google Scholar]
  2. F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for low Reynolds number swimmers: an example. J. Nonlinear Sci. 18 (2008) 277–302. [Google Scholar]
  3. H.C. Berg and R. Anderson, Bacteria swim by rotating their flagellar filaments. Nature 245 (1973) 380–382. [CrossRef] [PubMed] [Google Scholar]
  4. J. Blake, A finite model for ciliated micro-organisms. J. Biomech. 6 (1973) 133–140. [CrossRef] [PubMed] [Google Scholar]
  5. C. Brennen, An oscil lating-boundary-layer theory for ciliary propulsion. J. Fluid Mech. 65 (1974) 799–824. [CrossRef] [Google Scholar]
  6. P. Brunovský and C. Lobry, Contrôlabilité Bang Bang, contrôlabilité différentiable, et perturbation des systèmes non linéaires. Ann. Mat. Pura Appl. 105 (1975) 93–119. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Childress, Mechanics of swimming and flying, Cambridge Studies in Mathematical Biology 2. Cambridge University Press, Cambridge (1981). [Google Scholar]
  8. Y. Chitour, J.-M. Coron and M. Garavello, On conditions that prevent steady-state controllability of certain linear partial differential equations. Discrete Contin. Dyn. Syst. 14 (2006) 643–672. [CrossRef] [MathSciNet] [Google Scholar]
  9. G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations I: Linearized steady problems, Springer Tracts in Natural Philosophy 38. Springer-Verlag, New York (1994) [Google Scholar]
  10. K.A. Grasse and H.J. Sussmann, Global controllability by nice controls, in Nonlinear controllability and optimal control, Monogr. Textbooks Pure Appl. Math. 133, Dekker, New York (1990) 33–79. [Google Scholar]
  11. J. Happel and H. Brenner, Low Reynolds number hydrodynamics with special applications to particulate media. Prentice-Hall Inc., Englewood Cliffs, USA (1965). [Google Scholar]
  12. V. Jurdjevic, Geometric control theory, Cambridge Studies in Advanced Mathematics 52. Cambridge University Press, Cambridge (1997). [Google Scholar]
  13. V. Jurdjevic and I. Kupka, Control systems subordinated to a group action: accessibility. J. Differ. Equ. 39 (1980) 186–211. [Google Scholar]
  14. V. Jurdjevic and I. Kupka, Control systems on semi-simple Lie groups and their homogeneous sapces. Ann. Inst. Fourier 31 (1981) 151–179. [Google Scholar]
  15. V. Jurdjevic and G. Sallet, Controllability properties of affine systems. SIAM J. Contr. Opt. 22 (1984) 501–508. [CrossRef] [Google Scholar]
  16. S. Keller and T. Wu, A porous prolate-spheroidal model for ciliated micro-organisms. J. Fluid Mech. 80 (1977) 259–278. [CrossRef] [Google Scholar]
  17. J. Lighthill, Mathematical Biofluiddynamics, Regional Conference Series in Applied Mathematics 17. Society for Industrial and Applied Mathematics, Philadelphia, USA (1975). (Based on the lecture course delivered to the Mathematical Biofluiddynamics Research Conference of the National Science Foundation held from July 16–20 1973, at Rensselaer Polytechnic Institute, Troy, New York, USA.) [Google Scholar]
  18. E.M. Purcell, Life at low Reynolds numbers. Am. J. Phys. 45 (1977) 3–11. [CrossRef] [Google Scholar]
  19. J. San Martín, T. Takahashi and M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms. Quart. Appl. Math. 65 (2007) 405–424. [Google Scholar]
  20. J. Simon, Différentiation de problèmes aux limites par rapport au domaine. Lecture notes, University of Seville, Spain (1991). [Google Scholar]
  21. H.J. Sussmann, Some properties of vector field systems that are not altered by small perturbations. J. Differ. Equ. 20 (1976) 292–315. [Google Scholar]
  22. G. Taylor, Analysis of the swimming of microscopic organisms. Proc. Roy. Soc. London. Ser. A 209 (1951) 447–461. [Google Scholar]

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