Vortex Processes and Solid Body Dynamics

1. Mathematical Models of Electrical Conductivity Ferromagnetic Elements with Eddy Currents.- 1.1. Statements of the Problem.- 1.2. Asymptotic Solution of Unsteady Boundary-Value Problems for Magnetic and Electrical Fields.- 1.3. Eddy Currents Mathematical Model.- 1.4. General Equations of System Dynamics with External and Eddy Currents and Mechanical Degrees of Freedom.- 1.5. Mathematical Models of Stabilized Ferromagnetic Elements as Objects of Control.- 1.6. Mathematical Models of the Electromagnetic Levitation System Actuator.- 2. Mathematical Models of Stabilazed Objects with Compartments Containing Vortex Low-Viscous Liquid.- 2.1. Mathematical Models of a Solid Body with Cavity Partially Filled with Ideal Liquid.- 2.2. Velocity Field of LV Liquid Vortex Motion in a Moving Cavity.- 2.3. Generalized Forces and Derivatives of Liquid Kinetic Energy with Respect to Generalized Velocities.- 2.4. The Mathematical Model of a Solid Body with a Cavity Containing Vortex Low-Viscous Liquid.- 2.5. Axially Symmetric Body. Particular Cases of General Equations of Perturbed Motion.- 2.6. Axisymmetric Body. Coefficients Conversion Formulae.- 2.7. Axisymmetric Body. Derivation of Equations of the Body - Liquid System Perturbed Motion from the Variational Principle.- 2.8. Spacecraft with LPRE Stabilized Attitude.- 2.9. Spacecraft with LPRE, Slowly Rotating around Its Longitudial Axis.- 2.10. Determination of Hydrodynamic Coefficients.- 3. Analytical and Numerical Methods of Dynamics Investigation of Vehicles Described by Vortex Models.- 3.1. Preliminary Remarcs.- 3.2. Analytical Methods of Investigation. Harmonic Balance Method.- 3.3. An Algorithm for Numerical Solution of a Set of Integrodifferential Equations with a Singular Kernel of the Type (t ? ?)??2.- 3.4.Methodological Example.- 4. Experimental Verification of Mathematical Models for Eddy Currents and Vortex Motions of Liquid.- 4.1. Mathematical Models Used for Experimental Data Processing.- 4.2. Determination of Mathematical Model Parameters Based on Experimental Results.- 4.3. Scheme of the Experiment and Primary Processing of Results.- 4.4. Verification of Models for Eddy Currents in HECF Elements.- 4.5. Low-Viscous Liquid Vortex Motions Model Verification.- 5. Some Dynamics Problems for Systems with Electromagnetic Actuators.- 5.1. Characteristic Properties of Electromagnet as an Object of Control. Requirements to the Air Gap Regulation System.- 5.2. Mathematical Model of the Two-Mass System 'Controlled Electromagnet - Mass with Elasto-Viscous Suspension'.- 5.3. Measurements Composition Influence on Required Completeness of Controlled Electromagnet Mathematical Model.- 5.4. Eddy Currents Influence on Closed-Loop System Dynamics. Reduction of Integrodifferential Equations to an Equivalent Set of Differential Equations.- 6. Some Dynamics Problems for a Spacecrafts Having Compartments Partially Filled with Liquid.- 6.1. Stabilizability and Dynamic Stability of Spacecrafts Having Compartments Partially Filled with Liquid.- 6.2. Simplified Mathematical Models of Perturbed Motion for a Spacecraft Having Compartments Partially Filled with Liquid.- 6.3. Self-Sustained Oscillations in the Closed-Loop System 'Spacecraft - Liquid - Controller'.- 6.4. SC Stability in the Yaw Plane with Account of Potential and Vortex Motions of Liquid in Tanks.- 6.5. SC Stability in the Roll Plane for Non-Small Amplitudes of Angular Oscillations.- 7. Examples of Control Law Synthesis for an Object Described by a Vortex Model.- 7.1. A Control Law Allowing Hardware Implementation,Based on Air Gap Sensor and Current Transducer Indications.- 7.2. Synthesis of a Relay-Controller Closed-Loop System.- 7.3. Mathematical Modelling of Electromagnetic Levitation System Dynamics.- 8. Some Dynamics Problems for a Solid Body with Electrically Conductive Liquid Moving in Magnetic Field.- 8.1. Statements of the Problem. Main Assumptions.- 8.2. Magnetic Hydrodynamics Boundary-Value Problems for LVECF Liquid.- 8.3. Liquid - Magnetic Field System Kinetic Energy. Generalized Forces and Generalized Voltages.- 8.4. Equations of Dynamics for a Solid Body Containing LVECF Liquid with Related Magnetic Field Presence.- 8.5. Equations of Dynamics for a Solid Body with a Cavity of Revolution Having Narrow Internal Ribs.- 8.6. The Case of a Circular Cylinder-Shaped Cavity.- 8.7. Magnetic Field Influence on Solid Body - LVEC Liquid Open-Loop System Frequency Response.- 8.8. The Possibility of Using Magnetohydrodynamic Effects to Ensure Dynamic Stability of Spacecraft.- Conclusion.