Rigid Body Dynamics for Space Applications

Rigid Body Dynamics for Space Applications explores the modern problems of spaceflight mechanics, such as attitude dynamics of re-entry and space debris in Earth's atmosphere; dynamics and control of coaxial satellite gyrostats; deployment, dynamics, and control of a tether-assisted return mission of a re-entry capsule; and removal of large space debris by a tether tow.

Most space systems can be considered as a system of rigid bodies, with additional elastic and viscoelastic elements and fuel residuals in some cases. This guide shows the nature of the phenomena and explains the behavior of space objects. Researchers working on spacecraft attitude dynamics or space debris removal as well as those in the fields of mechanics, aerospace engineering, and aerospace science will benefit from this book.

• Provides a complete treatise of modeling attitude for a range of novel and modern attitude control problems of spaceflight mechanics
• Features chapters on the application of rigid body dynamics to atmospheric re-entries, tethered assisted re-entry, and tethered space debris removal
• Shows relatively simple ways of constructing mathematical models and analytical solutions describing the behavior of very complex material systems
• Uses modern methods of regular and chaotic dynamics to obtain results

Researchers and engineers working on spacecraft attitude dynamics and space debris removal; Graduate students studying astrodynamics or space engineering

Chapter 1: Mathematical Mechanical Preliminaries

• Abstract
• 1.1 Mathematics
• 1.2 Rigid Body Kinematic
• 1.3 Rigid Body Dynamics
• 1.4 Chaotic Motion

Chapter 2: Reentry Attitude Dynamics

• Abstract
• 2.1 Introduction
• 2.2 Aerodynamics of Reentry Vehicles
• 2.3 The Equations of Motion
• 2.4 Analytical Solutions of the Undisturbed Equation for Sinusoidal Aerodynamic Moment
• 2.5 Analytical Solutions of the Undisturbed Equation for Biharmonical Aerodynamic Moment
• 2.6 Quasistatic Solutions for the Disturbed Equation of Motion
• 2.7 Adiabatic Invariants and the Approximate Solution for the Disturbed Motion
• 2.8 Bifurcation and Ways of Its Elimination at the Descent of Spacecraft in the Rarefied Atmosphere
• 2.9 Chaotic Attitude Motion of Reentry Vehicle With an Internal Moving Mass
• 2.10 Chaotic Behavior of Bodies in a Resistant Medium
• 2.11 Chaotic Motion of a Reentry Capsule During Descent into the Atmosphere

Chapter 3: Dynamics and Control of Coaxial Satellite Gyrostats

• Abstract
• 3.1 Introduction
• 3.2 Attitude Motion Equations
• 3.3 Integrable Cases in the Dynamics of Coaxial Gyrostats
• 3.4 The Exact Analytical Solutions
• 3.5 Dynamics and Chaos Control of the Gyrostats
• 3.6 Dynamics and Control of Dual-Spin Gyrostat Spacecraft With Changing Structure
• 3.7 Adiabatic Invariants in the Dynamics of Axial Gyrostats

Chapter 4: Deployment, Dynamics, and Control of a Tether-Assisted Return Mission of a Reentry Capsule

• Abstract
• 4.1 Introduction
• 4.2 Mathematical Model of a Satellite With a Tethered Payload
• 4.3 Analytical Solution in the Case of a Slow Changing of the Parameters
• 4.4 Oscillations of the Satellite With a Vertical Elastic Tether
• 4.5 Oscillations in the Case of an Elliptic Orbit
• 4.6 Swing Principle for Deployment of a Tether-Assisted Return Mission of a Reentry Capsule
• 4.7 Tether-Assisted Return Mission From an Elliptical Orbit Taking Into Account Atmospheric Stage of Reentry

Chapter 5: Removal of Large Space Debris by a Tether Tow

• Abstract
• 5.1 Introduction
• 5.2 Dynamics of Orbital Debris Connected to Spacecraft by a Tether in a Free Space
• 5.3 Dynamics of Large Orbital Debris Removal Using Tethered Space Tug in the Earth's Gravitational Field
• 5.4 Behavior of Tethered Debris With Flexible Appendages
• 5.5 Dynamics, Analytical Solutions and Choice of Parameters for Towed Space Debris With Flexible Appendages
• 5.6 The Motion of Tethered Tug-Debris System With Fuel Residuals
• 5.7 Dynamics of Towed Large Space Debris Taking Into Account Atmospheric Disturbance
• 5.8 Chaos Behavior of Space Debris During Tethered Tow

Chapter 6: Original Tasks of Space Mechanics

• Abstract
• 6.1 Introduction
• 6.2 Gravitational Stabilization of the Satellite With a Moving Mass
• 6.3 The Dynamics of the Spacecraft of Variable Composition
• 6.4 Restoration of Attitude Motion of Satellite Using Small Numbers of Telemetry Measurements