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• W1840668691 abstract "Steady swimming can be characterized as both periodic and stable. These characteristics are the very definition of limit cycles, and so we ask Can we view swimming as a limit cycle? In this paper we will find that the answer is yes. We will define a class of dissipative systems which correspond to the passive dynamics of a body immersed in a Navier-Stokes fluid (i.e. the dynamics of a dead fish). Upon performing reduction by symmetry we will find a hyperbolically stable fixed point which corresponds to the stability of a dead fish in stagnant water. Given a periodic force on the shape of the body we will invoke the persistence theorem to assert the existence of a loop which approximately satisfies the exact equations of motion. If we lift this loop with a phase reconstruction formula we will find that the lifted loops are not loops, but stable trajectories which represent regular periodic motion reminiscent of swimming." @default.
• W1840668691 created "2016-06-24" @default.
• W1840668691 creator A5058709078 @default.
• W1840668691 date "2012-11-12" @default.
• W1840668691 modified "2023-09-27" @default.
• W1840668691 title "Swimming as a limit cycle" @default.
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• W1840668691 hasPublicationYear "2012" @default.
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