Swimming in curved space or The Baron and the cat

Abstract

We study the swimming of non-relativistic deformable bodies in (empty) static curved spaces. We focus on the case where the ambient geometry allows for rigid body motions. In this case the swimming equations turn out to be geometric. For a small swimmer, the swimming distance in one stroke is determined by the Riemann curvature times certain moments of the swimmer.

arXiv comment19 pages 6 figures

References in corpus (2)

• "Swimming" versus "swinging" in spacetime
• Optimal rotations of deformable bodies and orbits in magnetic fields

Cited by in corpus (5)

• Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity
• Rotational random walk of the harmonic three body system
• Extended-body motion in black hole spacetimes: What is possible?
• Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies
• Locomotion without force, and impulse via dissipation: Robotic swimming in curved space via geometric phase