Control of Fluid-Containing Rotating Rigid Bodies

 Content: 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
 Abstract:             \"This book is devoted to the study of the dynamics of rotating bodies with cavities containing liquid. Two basic classes of motion are analyzed: rotation and libration. Cases of complete and partial filling of cavities with ideal liquid and complete filling with viscous liquid are treated. A method is presented for obtaining relations between angular velocities perpendicular to main rotation and external force momentums, treated as control. This work will be of interest to professionals and researchers at universities and laboratories specializing in problems of control for hybrid systems and aerospace/mechanical engineering, as well as to under-/postgraduates with this specialization\"