The dynamics of the weakly perturbed motion of a liquid-filled gyroscope and the control problem

Gurchenkov, A. A.; Korneyev, V.V.; Nosov, M. V.

doi:10.1016/j.jappmathmech.2009.01.012

Cited by 1 publication

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“…In Ref. [69], the Cauchy problem was considered in a linear formulation for the perturbed relatively uniform rotation of the motion of a dynamically symmetric rigid body with a cavity filled with an ideal fluid. The problem of jointly solving the equations of hydrodynamics and solid mechanics was reduced to solving an eigenvalue problem that depended only on the geometry of the cavity and the subsequent integration of a system of differential equations.…”

Section: Dynamics Of Ideal Rotating Incompressible and Stratified Non...mentioning

confidence: 99%

Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

Gurchenkov,

Matveev

2024

Physics

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Since the middle of the 20th century, an understanding of the diversity of the natural magnetohydrodynamic phenomena surrounding us has begun to emerge. Magnetohydrodynamic nature manifests itself in such seemingly heterogeneous processes as the flow of water in the world’s oceans, the movements of Earth’s liquid core, the dynamics of the solar magnetosphere and galactic electromagnetic fields. Their close relationship and multifaceted influence on human life are becoming more and more clearly revealed. The study of these phenomena requires the development of theory both fundamental and analytical, unifying a wide range of phenomena, and specialized areas that describe specific processes. The theory of translational fluid motion is well developed, but for most natural phenomena, this condition leads to a rather limited model. The fluid motion in the cavity of a rotating body such that the Coriolis forces are significant has been studied much less. A distinctive feature of the problems under consideration is their significant nonlinearity, (i.e., the absence of a linear approximation that allows one to obtain nontrivial useful results). From this point of view, the studies presented here were selected. This review presents studies on the movements of ideal and viscous fluids without taking into account electromagnetic phenomena (non-conducting, non-magnetic fluid) and while taking them into account (conducting fluid). Much attention is payed to the macroscopic movements of sea water (conducting liquid) located in Earth’s magnetic field, which spawns electric currents and, as a result, an induced magnetic field. Exploring the processes of generating magnetic fields in the moving turbulent flows of conducting fluid in the frame of dynamic systems with distributed parameters allows better understanding of the origin of cosmic magnetic fields (those of planets, stars, and galaxies). Various approaches are presented for rotational and librational movements. In particular, an analytical solution of three-dimensional unsteady magnetohydrodynamic equations for problems in a plane-parallel configuration is presented.

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Section: Dynamics Of Ideal Rotating Incompressible and Stratified Non...mentioning

confidence: 99%

Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

Gurchenkov,

Matveev

2024

Physics

View full text Add to dashboard Cite

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The dynamics of the weakly perturbed motion of a liquid-filled gyroscope and the control problem

Cited by 1 publication

References 2 publications

Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

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