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arXiv · 1905.11002

Optimal dynamics of a spherical squirmer in Eulerian description

Victor P. Ruban
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Abstract

The problem of optimization of a cycle of tangential deformations of the surface of a spherical object (microsquirmer) self-propelling in a viscous fluid at low Reynolds numbers is represented in a noncanonical Hamiltonian form. The evolution system of equations for the coefficients of expansion of the surface velocity in the associated Legendre polynomials $P^1_n(\cos\theta)$ is obtained. The system is quadratically nonlinear, but it is integrable in the three-mode approximation. This allows a theoretical interpretation of numerical results previously obtained for this problem.

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Victor P. Ruban. 2019-05-27. Optimal dynamics of a spherical squirmer in Eulerian description. https://doi.org/10.1134/s0021364019080101

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