Introductory Attitude Dynamics

From the preface: "The present text deals with attitude dynamics and is devoted to satellites of finite size. It begins with a discussion of the inertia moment tensor, Euler's law, Euler's angles, Euler's equations, and Euler's frequencies. After that a thorough treatment of the concept of centre of gravity versus centre of mass is given. After libration has been discussed and gyrodynamics proper has been dealt with, the attitude of the moment-free satellite, including the gyrostat, is studied. Particular attention is paid to the attitude behaviour of torquefree single and dual spinners, and the new collinearity theorems are introduced and explored to predict attitude stability and attitude drift. The derivation of each significant formula is followed by the discussion of a practical sample problem in order to acquaint the student with typical situations, typical results, and typical numerical values. There are numerous problems following each chapter. The most important data and the answers to the problems are compiled in appendices."

1 The Gyroscope.- 1.1 Angular Momentum.- 1.2 Time Derivative of Angular Momentum.- 1.3 Inertia Tensor.- 1.4 The Huygens-Steiner Parallel Axes Theorem.- 1.5 Principal Inertia Moments.- 1.6 Kinetic Energy.- 1.7 Euler Equations.- 1.8 Euler Equations for Principal Axes.- 1.9 Euler Angles.- 1.10 Coordinate Transformation.- 1.11 Coordinate Transformation of Angular Velocities.- 1.12 Integrability.- 1.13 The Magnus Shape Triangle.- Suggested Reading.- Problems.- 2 Center of Gravity.- 2.1 Rod Satellite.- 2.2 Small Rod Satellite.- 2.3 Center of Gravity for a Small Satellite, General Case.- 2.4 Kepler Force for a Small Satellite.- 2.5 Torque about Mass Center, General Case.- 2.6 Potential.- 2.7 Locked Rotation.- 2.8 Orbital Period for Locked Rotation.- 2.9 Spacecraft with Booms.- 2.10 Microgravity.- Suggested Reading.- Problems.- 3 Libration.- 3.1 Libration about Position Vector and within Orbital Plane.- 3.2 Libration about Position Vector and Normal to the Orbital Plane.- 3.3 Libration about Tangent to Orbit and Normal to the Orbital Plane.- 3.4 Attitude Change about Tangent and within Orbital Plane.- 3.5 Attitude Stability.- 3.6 Libration of the Moon.- Suggested Reading.- Problems.- 4 Stability of Satellite Attitude in a Central Force Field.- 4.1 Cardan Angles.- 4.2 Spinning Axisymmetric Satellite.- 4.3 Arbitrary Satellite in Locked Rotation.- 4.4 Arbitrary Satellite on Elliptical Orbit in Quasi-Locked Rotation.- Suggested Reading.- Problems.- 5 Torquefree Gyros.- 5.1 Solution of Euler Equations for Torquefree Gyros.- 5.2 Phase Plane Representation.- 5.3 Kinetic Energy Ellipsoid and Poinsot Ellipsoid.- 5.4 Angular Momentum Ellipsoid.- 5.5 MacCullagh Ellipsoid.- 5.6 Velocity and Acceleration of an Arbitrary Point within a Torquefree Gyro.- 5.7 Stability of Rotation about a Principal Axis for a Rigid Gyro.- 5.8 Stability of Rotation about a Principal Axis for a Deformable Gyro.- 5.9 Collinearity Theorems.- Suggested Reading.- Problems.- 6 Torquefree Axisymmetric Gyros.- 6.1 Angular Velocity Components.- 6.2 Euler Frequencies.- 6.3 Velocity and Acceleration of a Point.- 6.4 The Inertial Force Field.- 6.5 Changing Inertia Moments.- 6.6 Capture.- Suggested Reading.- Problems.- 7 Deformable Axisymmetric Gyros.- 7.1 The Single Solid Body.- 7.2 The Axisymmetric Solid Body.- 7.3 Observations.- 7.4 Floating Coordinates.- 7.5 Auxiliary Inertia Products and Moments.- 7.6 Angular Momentum of a Deforming Body.- 7.7 Kinetic Energy of Rotation of a Deforming Body.- 7.8 Energy Rates.- 7.9 Application to a Constrained System with ?z = 0.- 7.10 Application to a Constrained System with ?u = ?v = 0.- 7.11 Conclusions.- Suggested Reading.- Problems.- 8 Secular Attitude Drift of a Torquefree Dissipative Axisymmetric Gyro.- 8.1 Attitude Drift Rate and Attitude Stability.- 8.2 The Attitude Drift Process.- 8.3 Circles in the vz-Plane.- 8.4 Arbitrary Initial and Stable Final State.- 8.5 Elastic Deformation and Attitude Stability.- 8.6 Effect of Deformation on Angular Velocities.- 8.7 Effect of Deformation on Kinetic Energy and Strain Energy.- Suggested Reading.- Problems.- 9 Despin.- 9.1 Despin by Yo-Yo Masses.- 9.2 Despin by Boom Extension.- 9.3 Eccentric Installation.- 9.4 Configuration Change Terms in Euler Equations.- Suggested Reading.- Problems.- 10 Torque about Body-Fixed Axes of an Axisymmetric Gyro.- 10.1 Torque Perpendicular to Axis of Symmetry.- 10.2 Torque about Axis of Symmetry.- Suggested Reading.- Problems.- 11 Rigid Gyrostats.- 11.1 Angular Momentum and Euler Equations.- 11.2 Attitude Stability in the Short Run of Torquefree Gyrostat.- 11.3 Torquefree Axisymmetric Gyrostats.- 11.4 Bearing Friction.- 11.5 Euler Angles for a Torquefree Axisymmetric Gyrostat.- 11.6 The Inertial Force Fields.- 11.7 Spinning Axisymmetric Gyrostat in a Central Force Field.- Suggested Reading.- Problems.- 12 Torquefree Dissipative Axisymmetric Gyrostats.- 12.1 Near-Rigid Rotors and Platforms.- 12.2 Secular Attitude Drift for a Torquefree Axisymmetric Gyrostat with Dissipative Platform.- 12.3 Secular Attitude Drift for a Torquefree Axisymmetric Gyrostat with Dissipative Rotor.- 12.4 Secular Attitude Drift for a Torquefree Axisymmetric Gyrostat with Dissipative Rotor and Dissipative Platform.- Suggested Reading.- Problems.- Appendix A: Euler Angles.- Appendix B: Euler Parameters.- Appendix C: Cardan Angles.- Appendix D: Engineering Data.- Appendix E: Nomenclature.- Appendix F: Answers to Selected Problems.- Author Index.