TY - GEN
T1 - Dynamics of a solid affected by a pulsating point source of fluid
AU - Morgulis, Andrey
AU - Vladimirov, Vladimir
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
KW - Analytical dynamics
KW - Björknes's force
KW - Pulsating point source of fluid
KW - Solid body
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U2 - 10.1007/978-1-4020-6744-0_12
DO - 10.1007/978-1-4020-6744-0_12
M3 - Conference contribution
AN - SCOPUS:77957147616
SN - 9781402067433
T3 - Solid Mechanics and its Applications
SP - 135
EP - 150
BT - IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium
PB - Springer Verlag
T2 - IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
Y2 - 25 August 2006 through 30 August 2006
ER -