Control of Fluid-Containing Rotating Rigid Bodies

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ISBN 9781138000216
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Features

- Provides a solution of the problem of stability of a free rotation of rigid body with a store of liquid in a cylindrical cavity.
- Allows Hamilton-Pontryagin formalism to be employed for the formulation of a broad class of optimal control problems for rotating bodies with liquid.
- Uses the model of a flat wall to take into account the influence of viscosity on the dynamics of a rotating solid body with liquid.
- Developed models and methods can be used for studying the dynamics of aircraft in the atmosphere and of spacecraft with stores of liquid fuel

Summary

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.

Table of 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(s)

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.