Geometric Aspects of Force Controllability for a Swimming Model
- 41 Downloads
We study controllability properties (swimming capabilities) of a mathematical model of an abstract object which “swims” in the 2-D Stokes fluid. Our goal is to investigate how the geometric shape of this object affects the forces acting upon it. Such problems are of interest in biology and engineering applications dealing with propulsion systems in fluids.
KeywordsStokes equation Swimming model Coupled systems Multiplicative control Controllability
Unable to display preview. Download preview PDF.
- 5.Hirose, S.: Biologically Inspired Robots: Snake-like Locomotors and Manipulators. Oxford University Press, Oxford (1993) Google Scholar
- 6.Khapalov, A.Y.: Bilinear control for global controllability of the semilinear parabolic equations with superlinear terms, the Special volume “Control of Nonlinear Distributed Parameter Systems,” dedicated to D. Russell, G. Chen, I. Lasiecka, J. Zhou (eds.) pp. 139–155. Dekker (2001) Google Scholar
- 10.Khapalov, A.Y.: The well-posedness of a model of an apparatus swimming in the 2-D Stokes fluid, preprint. Available as Techn. Rep. 2005-5, Washington State University, Department of Mathematics, http://www.math.wsu.edu/TRS/2005-5.pdf
- 13.Lighthill, M.J.: Mathematics of Biofluiddynamics. Society for Industrial and Applied Mathematics, Philadelphia (1975) Google Scholar
- 14.McIsaac, K.A., Ostrowski, J.P.: Motion planning for dynamic eel-like robots. In Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, pp. 1695–1700 (2000) Google Scholar
- 15.Martinez, S., Cortés, J.: Geometric control of robotic locomotion systems, In Proc. X Fall Workshop on Geometry and Physics, Madrid, 2001, Publ. de la RSME, vol. 4, pp. 183–198 (2001) Google Scholar
- 17.Peskin, C.S., McQueen, D.M.: A general method for the computer simulation of biological systems interacting with fluids. SEB Symposium on biological fluid dynamics, Leeds, England, 5–8 July 1994 Google Scholar
- 18.Symon, K.R.: Mechanics. Addison–Wesley, Reading (1971) Google Scholar