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Control of Fluid-Containing Rotating Rigid Bodies

By Anatoly A. Gurchenkov, Mikhail V. Nosov, Vladimir I. Tsurkov

CRC Press – 2013 – 160 pages

Series: Communications in Cybernetics, Systems Science and Engineering

Purchasing Options:

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    978-1-13-800021-6
    April 11th 2013

Description

This book is devoted to the study of the dynamics of rotating bodies with cavities containing liquid. Two basic classes of motions are analyzed: rotation and libration. Cases of complete and partial filling of cavities with ideal liquid and complete filling with viscous liquid are treated. The volume presents a method for obtaining relations between angular velocities perpendicular to main rotation and external force momentums, which are treated as control.

The developed models and methods of solving dynamical problems as well as numerical methods for solving problems of optimal control can be used for studying the dynamics of aircraft in the atmosphere and spacecraft with stores of liquid fuel, which are rotating around some axis for stabilization. The results are also applicable in the development of fast revolving rotors, centrifuges and gyroscopes, which have cavities filled with liquid.

This work will be of interest to researchers at universities and laboratories specializing in problems of control for hybrid systems, as well as to under-/postgraduates with this specialization. It will also benefit researchers and practitioners in aerospace and mechanical engineering.

Contents

Introduction

Control of a rotating rigid body with a cavity completely filled with an ideal fluid

Equations of motion of a rigid body with a cavity completely filled with an ideal incompressible fluid

Stability of the steady rotation of a solid body with a cavity containing a fluid

The dependence of the angular velocity of the perturbed motion on the moment of external forces

An equivalent system of equations convenient for studying optimal control problems

An example with discontinuous control

Application of Bellman's optimality principle

Reduction of the main relation to a fourth-order system

Control of a rotating rigid body containing a fluid with free surface

Statement of the problem

Small oscillations of a viscous fluid partially filling a vessel

Rotational motions of a rigid body with a cavity partially filled with a fluid

Linearization of the problem

Hydrodynamic problem

The Bubnov-Galerkin method

Stability of the free rotation of a body-fluid system

Equations of motion of a body-fluid system in an equivalent form

Oscillations of a plate in a viscous fluid: The flat wall model

An unsteady boundary layer on a rotating plate

Longitudinal quasi-harmonic oscillations of a plate

Boundary layer structure

Tangential stress vector

Oscillatory solutions

Oscillations of a viscous incompressible fluid above a porous plate in the presence of medium injection (suction)

Motion of the plate with a constant acceleration

Control of a rotating rigid body containing a viscous fluid

Small oscillations of a viscous fluid completely filling a vessel

Equations of the perturbed motion of a body with a cavity containing a viscous fluid

Coefficients of inertial couplings of a rigid body with a fluid: the case of a cylindrical cavity

Oscillations of a viscous incompressible fluid in a cavity of a rotating body

Internal friction moment in a fluid-filled gyroscope

Stability of a fluid-filled gyroscope

Equations of motion for a rigid body with a cavity equipped with fluid oscillation dampers

An integral relation in the case of a viscous fluid

An equivalent system in the optimal control setting

Conclusion

Author Bio

Anatoly A. Gurchenkov, Doctor of Science (in physics and mathematics), Leading Researcher at the Department of Complex Systems, Computer Center, Russian Academy of Sciences and Professor at the Russian State Technological University (MATI). A well-known specialist in stability and control of rotating dynamic systems with a fluid-filled cavity. Author of more than 100 papers published by the Russian Academy of Sciences, “Fizmatlit’’ and other publishing houses, including four monographs; author of two patents.

Mikhail V. Nosov, Candidate of Science (in physics and mathematics), Senior Researcher at the Department of Complex Systems, Computer Center, Russian Academy of Sciences. Author of more than 25 papers published by the Russian Academy of Sciences and other publishing houses. Teaches courses in programming, computer science, and theory of relational databases at the Russian State Technological University (MATI).

Vladimir I. Tsurkov, Doctor of Science (in physics and mathematics), Head of the Department of Complex Systems Computer Center, Russian Academy of Sciences, and Professor at the Moscow Institute of Physics and Technology. Member of the Institute for Management Sciences and Operations Research (USA), Associate Member of the Russian Academy of Natural Sciences, Member of the Editorial Board of the Journal of Computer and Systems Sciences International. One of the leading experts in aggregation-based decomposition methods and a well-known specialist in analysis of numerical methods related to operation research models, in large-scale hierarchical optimization and control, and in catastrophe theory. Author of more than 180 papers published by the Russian Academy of Sciences, “Fizmatlit" and other publishing houses (in particular, Kluwer), including six monographs.

Name: Control of Fluid-Containing Rotating Rigid Bodies (Hardback)CRC Press 
Description: By Anatoly A. Gurchenkov, Mikhail V. Nosov, Vladimir I. Tsurkov. This book is devoted to the study of the dynamics of rotating bodies with cavities containing liquid. Two basic classes of motions are analyzed: rotation and libration. Cases of complete and partial filling of cavities with ideal liquid and complete...
Categories: Fluid Mechanics, Fluid Dynamics, Industrial Engineering & Manufacturing, Mathematics & Statistics for Engineers