Dynamics of a solid affected by a pulsating point source of fluid

Andrey Morgulis*, Vladimir Vladimirov

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


This paper provides a new insight to the classical Björknes's problem. We examine a mechanical system "solid+fluid" consisted of a solid and a point source (singlet) of fluid, whose intensity is a given function of time. First we show that this system is governed by the least action (Hamilton's) principle and derive an explicit expression for the Lagrangian in terms of the Green function of the solid. The Lagrangian contains a linear in velocity term. We prove that it does not produce a gyroscopic force only in the case of a spherical solid. Then we consider the periodical high-frequency pulsations (vibrations) of the singlet. In order to construct the high-frequency asymptotic solution we employ a version of the multiple scale method that allows us to obtain the "slow" Lagrangian for the averaged motions directly from Hamilton's principle. We derive such a "slow" Lagrangian for a general solid. In details, we study the "slow" dynamics of a spherical solid, which can be either homogeneous or inhomogeneous in density. Finally, we discuss the "Björknes's dynamic buoyancy" for a solid of general form.

Original languageEnglish
Title of host publicationIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9781402067433
Publication statusPublished - 2008
Externally publishedYes
EventIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Moscow, Russian Federation
Duration: Aug 25 2006Aug 30 2006

Publication series

NameSolid Mechanics and its Applications
ISSN (Print)1875-3507


OtherIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
Country/TerritoryRussian Federation


  • Analytical dynamics
  • Björknes's force
  • Pulsating point source of fluid
  • Solid body

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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