DYNAMICS OF ROTATION: AN ELEMENTARY INTRODUCTION TO RIGID DYNAMICS

By N. JALIL

1 Mathematical Mechanical Preliminaries 1 11 Mathematics 1 12 Rigid Body Kinematic 6 13 Rigid Body Dynamics 13 14 Chaotic Motion 17 References 23 2 Reentry Attitude Dynamics 25 21 Introduction 25 22 Aerodynamics of Reentry Vehicles 26 23 The Equations of Motion 33 24 Analytical Solutions of the Undisturbed Equation for Sinusoidal Aerodynamic Moment 44 25 Analytical Solutions of the Undisturbed Equation for Biharmonical Aerodynamic Moment 49 26 Quasistatic Solutions for the Disturbed Equation of Motion 59 27 Adiabatic Invariants and the Approximate Solution for the Disturbed Motion 60 28 Bifurcation and Ways of Its Elimination at the Descent of Spacecraft in the Rarefied Atmosphere 68 29 Chaotic Attitude Motion of Reentry Vehicle With an Internal Moving Mass 85 210 Chaotic Behavior of Bodies in a Resistant Medium 94 211 Chaotic Motion of a Reentry Capsule During Descent into the Atmosphere 109 References 121 3 Dynamics and Control of Coaxial Satellite Gyrostats 127 31 Introduction 127 32 Attitude Motion Equations 129 33 Integrable Cases in the Dynamics of Coaxial Gyrostats 135 34 The Exact Analytical Solutions 141 35 Dynamics and Chaos Control of the Gyrostats 153 36 Dynamics and Control of Dual-Spin Gyrostat Spacecraft With Changing Structure 159 37 Adiabatic Invariants in the Dynamics of Axial Gyrostats 166 References 175 4 Deployment, Dynamics, and Control of a Tether-Assisted Return Mission of a Reentry Capsule 179 41 Introduction 179 42 Mathematical Model of a Satellite With a Tethered Payload 182 43 Analytical Solution in the Case of a Slow Changing of the Parameters 192 44 Oscillations of the Satellite With a Vertical Elastic Tether 202 45 Oscillations in the Case of an Elliptic Orbit 220 46 Swing Principle for Deployment of a Tether-Assisted Return Mission of a Reentry Capsule 230 47 Tether-Assisted Return Mission From an Elliptical Orbit Taking Into Account Atmospheric Stage of Reentry 240 References 250 5 Removal of Large Space Debris by a Tether Tow 255 51 Introduction 255 52 Dynamics of Orbital Debris Connected to Spacecraft by a Tether in a Free Space 256 53 Dynamics of Large Orbital Debris Removal Using Tethered Space Tug in the Earth’s Gravitational Field 271 54 Behavior of Tethered Debris With Flexible Appendages 286 55 Dynamics, Analytical Solutions and Choice of Parameters for Towed Space Debris With Flexible Appendages 295 56 The Motion of Tethered Tug-Debris System With Fuel Residuals 308 57 Dynamics of Towed Large Space Debris Taking Into Account Atmospheric Disturbance 323 58 Chaos Behavior of Space Debris During Tethered Tow 342 References 353 6 Original Tasks of Space Mechanics 357 61 Introduction 357 62 Gravitational Stabilization of the Satellite With a Moving Mass 358 63 The Dynamics of the Spacecraft of Variable Composition 371 64 Restoration of Attitude Motion of Satellite Using Small Numbers of Telemetry Measurements 383 References 399