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Symmetry, Reduction and Swimming in a Perfect Fluid


Radford, James Edward (2003) Symmetry, Reduction and Swimming in a Perfect Fluid. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/CE65-XM80.


This thesis presents a geometric picture of a deformable body in a perfect fluid and a way to approximate its dynamics and the motion, resulting from cyclic shape deformations, of the body and, interestingly, the fluid as well. Emphasis is placed on the group structure of the configuration space of the body fluid system and the resulting symmetry in their equations of motion. Symmetry is also used to reduce a series expansion for the flow of a time dependent vector field in order to obtain a novel expansion for the path-ordered exponential. This can be used to approximate holonomy, or geometric phase, in a principal bundle when its evolution is governed by a connection on the bundle and it is subject to periodic shape inputs. Simple models for swimming in and the stirring of a perfect fluid are proposed and examined.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:deformable body; fluid dynamics; geometry; path ordered exponential; reduction; rigid body; symmetry
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Burdick, Joel Wakeman
Thesis Committee:
  • Burdick, Joel Wakeman (chair)
  • Brennen, Christopher E.
  • Marsden, Jerrold E.
  • Murray, Richard M.
Defense Date:23 May 2003
Record Number:CaltechETD:etd-06042003-181857
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2431
Deposited By: Imported from ETD-db
Deposited On:14 Oct 2004
Last Modified:13 May 2021 22:47

Thesis Files

PDF (Radford_je_2003.pdf) - Final Version
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