Dynamics of a Solid Affected by a Pulsating Point Source of Fluid.

TY - CHAP

T1 - Dynamics of a Solid Affected by a Pulsating Point Source of Fluid.

AU - Vladimirov, Vladimir A.

AU - Morgulis, Andrey

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 - Fluid Dynamics

UR - http://www.scopus.com/inward/record.url?scp=77957147616&partnerID=8YFLogxK

U2 - 10.1007/978-1-4020-6744-0_12

DO - 10.1007/978-1-4020-6744-0_12

M3 - Chapter

SN - 978-1-4020-6743-3

VL - 6

T3 - IUTAM Bookseries

SP - 135

EP - 150

BT - Regular and Chaotic Dynamics

A2 - Borisov, Alexey

A2 - Kozlov, Valery

A2 - Mamaev, Ivan

A2 - Sokolovskiy, Mikhail

PB - Springer

ER -