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  1. Journal of Mathematical Fluid Mechanics
  2. Journal of Mathematical Fluid Mechanics : Volume 7
  3. Journal of Mathematical Fluid Mechanics : Volume 7, Issue 3, Supplement,August 2005
  4. On Vibrodynamics of Pendulum and Submerged Solid
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Journal of Mathematical Fluid Mechanics : Volume 19
Journal of Mathematical Fluid Mechanics : Volume 18
Journal of Mathematical Fluid Mechanics : Volume 17
Journal of Mathematical Fluid Mechanics : Volume 16
Journal of Mathematical Fluid Mechanics : Volume 15
Journal of Mathematical Fluid Mechanics : Volume 14
Journal of Mathematical Fluid Mechanics : Volume 13
Journal of Mathematical Fluid Mechanics : Volume 12
Journal of Mathematical Fluid Mechanics : Volume 11
Journal of Mathematical Fluid Mechanics : Volume 10
Journal of Mathematical Fluid Mechanics : Volume 9
Journal of Mathematical Fluid Mechanics : Volume 8
Journal of Mathematical Fluid Mechanics : Volume 7
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 4, November 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 3, Supplement,August 2005
Topics in an Ideal Fluid Dynamics
Solutions with Concentration to the Riemann Problem for the One-Dimensional Chaplygin Gas Equations
Regularity in an Unusual Variational Problem
Existence of Multimodal Standing Gravity Waves
Asymptotic Directions, Monge–Ampère Equations and the Geometry of Diffeomorphism Groups
On Stability of a Regular Vortex Polygon in the Circular Domain
Microglobal Analysis of the Euler Equations
On Vibrodynamics of Pendulum and Submerged Solid
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 3, August 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 2, Supplement,May 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 2, May 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 1, Supplement,March 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 1, March 2005
Journal of Mathematical Fluid Mechanics : Volume 6
Journal of Mathematical Fluid Mechanics : Volume 5
Journal of Mathematical Fluid Mechanics : Volume 4
Journal of Mathematical Fluid Mechanics : Volume 3
Journal of Mathematical Fluid Mechanics : Volume 2
Journal of Mathematical Fluid Mechanics : Volume 1

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On Vibrodynamics of Pendulum and Submerged Solid

Content Provider SpringerLink
Author Vladimirov, V. A.
Copyright Year 2005
Abstract The paper is devoted to the studying of a dynamical system ‘solid + fluid’ in the presence of vibrations using the Van-der-Pol–Krylov–Bogoliubov (VPKB) averaging method. The main result of the paper is the discovery of a close similarity between a classical pendulum and a system of ‘inhomogeneous solid + fluid’ in the presence of vibrations. First, we consider the celebrated example of the Stephenson–Kapitza pendulum using the least action formulation of the VPKB averaging method. The method directly exploits the least action principle, in which an averaging procedure appears most naturally and conservation laws follow automatically. Its main advantage is a substantial decrease of the required amount of analytical calculations, which are typically cumbersome for the VPKB averaging method. Then, we consider the dynamics of a rigid sphere in an inviscid incompressible fluid, which fills a vibrating vessel of an arbitrary shape. The sphere can be either homogeneous or inhomogeneous in density. The results provide a full model for the averaged (or ‘slow’) motions, which includes the ‘slow Lagrangians’, the ‘slow potential energy’, and the ‘vibrogenic’ force, exerted by a surrounding fluid on a solid. We outline our calculations, present results in general forms, and briefly discuss related examples, properties, and conjectures.
Ending Page S412
Starting Page S397
File Format PDF
ISSN 14226928
e-ISSN 14226952
Journal Journal of Mathematical Fluid Mechanics
Issue Number 3
Volume Number 7
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2005-01-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Vibrations Mechanics, Fluids, Thermodynamics Mathematical Methods in Physics Fluids solids Asymptotic methods, singular perturbations averaging method fluids Averaging of perturbations
Content Type Text
Resource Type Article
Subject Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics
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