JETP Letters

, Volume 109, Issue 8, pp 512–515 | Cite as

Optimal Dynamics of a Spherical Squirmer in Eulerian Description

  • V. P. RubanEmail author
Plasma, Hydro- and Gas Dynamics


The problem of optimization of a cycle of tangential deformations of the surface of a spherical object (micro-squirmer) 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 \(P_n^1(\rm{cos}\;\theta)\) 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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© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

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