DYNAMIC ANALYSIS OF SPACE TETHER MISSIONS

Transcription

1 DYNAMIC ANALYSIS OF SPACE TETHER MISSIONS Volume 126 ADVANCES IN THE ASTRONAUTICAL SCIENCES by Eu gene M. Levin Published for the American Astronautical Society by Univelt, Incorporated, P.O. Box 28130, San Diego, California Web Site:

2 Copyright 2007 by AMERICAN ASTRONAUTICAL SOCIETY AAS Publications Office P.O. Box San Diego, California Affiliated with the American Association for the Advancement of Science Member of the International Astronautical Federation First Printing 2007 Library of Congress Card No ISSN ISBN (Hard Cover) ISBN (Soft Cover) Published for the American Astronautical Society by Univelt, Incorporated, P.O. Box 28130, San Diego, California Web Site: Printed and Bound in the U.S.A. vi

3 CONTENTS Foreword iii About the Book NEW MISSIONS FOR SPACE TETHERS HARPOONING A COMET COMET NUCLEUS SAMPLE RETURN Nomenclature Race to Comets and Asteroids Tether-Mediated Sample Retrieval Spacecraft Motion in the Vicinity of the Comet Dynamic Models and Equations Hovering and Close Approach Trajectories Equations of Tethered Motion Equations in a Newtonian Form Equations in Minakov s Form Equations for the Tangent Orientation Angles Calculation of the Tether Tension Normalization of the Arclength Tether Deployment Tether Tension Range Deployment Dynamics Energy Considerations Tether Retrieval Retrieval Dynamics Dynamics of a Capsule Moving Along the Tether Other Scenarios Tether Safety Conclusions

4 2 CONTENTS 2. SURVIVING IN SPACE TETHER PHYSICS AND SURVIVABILITY EXPERIMENT.. 63 Nomenclature The Story of Survival Evolution Model Equations of Motiom Internal Friction in the Tether Pendular Motions Forms of Small OScillations Modal Decomposition Equations of Libration Evolution Equations Non-Resonant Motions Resonant Motions Poincare Maps and Resonance Zones Evolution in the Resonance Zone Deployment Dynamics Deployment and the Resonances Tether Bow During and After Deployment Thermal Effects Thermal Hysteresis Thermal Cycles and Libration Evolution Rotation of the End-Bodies Alignment of the Spin Axis Torsional Oscillations Interaction with Transverse Waves in the Tether Conclusions SAVING A SPACE STATION MIR ELECTRODYNAMIC TETHER SYSTEM Nomenclature Space Station in Trouble Electrodynamic System Model Equations of Motion Tether Heating Electric Current in the Tether Geomagnetic Field Model Calculating Geomagnetic Field Along the Orbit Pendular Motions Equations of Pendular Motion Operation Modes System Characteristics

5 CONTENTS Librational Instability Out-of-plane Instability In-plane Instability Libration Control Attitude Dynamics of the Space Station Equations of Mir s Rotation Relative Equilibrium Small Oscillations Resonant and Non-Resonant Motions Limitations on Tether Libration AMplitudes Spectral Analysis of Free Oscillations Spectral Analysis of Forced Oscillations Non-Resonant Motions Resonant Motions Attitude Control Gyro-Damping Attitude Control with Thrusters Transverse Oscillations of the Tether Equations of Transverse Oscillations Linear Oscillations Modal Decomposition The Effect of Transverse Oscillations on Mir s Rotation Controlling Transverse Oscillations Torsional Oscillations of the Tether Rotation of the End-Body Equations of Torsional Motion Torsional Eignefrequencies Evolution of Motion Thermal Effects Longitudinal Damper Tether State Estimation Conclusions GOING FOR A SPIN ELECTRODYNAMIC DELIVERY EXPRESS Nomenclature Perpetuum Tether Mobile Dynamic Model Newtonian Formulation Motion of the Center of Mass Tether Rotation Small Oscillations Minakov s Formulation

6 4 CONTENTS 4.3. Operation of a Spinning Tether System Electrodynamic Thrust Magnetic Field Along the Orbit Evolution of the Spin Axis Tether Oscillations and Stability Control of the Spinning Tether System Orbit Transfers with Spinning Tethers Equations of Orbit Evolution Optimal Current Scheduling Average Performance Characteristics Fastest Orbital Plane Change Orbital Plane Change Assisted by Altitude Change Fastest In-Plane Orbit Transfers Elliptic Orbits with High Apogees Attitude Motion of the End-Bodies Conclusions CATCHING A PAYLOAD MOMENTUM EXCHANGE ELECTRODYNAMIC REBOOST SYSTEM Nomenclature Electrodynamic Tether Transport Dynamic Model Equations of Motion Gravitational Field Model Stationary Rotation Natural Forms of Oscillations Equations of Small Oscillations The Eigenvalue Problem Eigenforms and Eigenvalues Decomposition of Motion General Equations Calculation of the Integrals of Tension The Case of a Perfectly Tapered Tether Coupled Longitudinal-Transverse Oscillations Gravitational Forces Expansion of the Newtonian Term General Power Series Expansion Contribution of the Higher Order Terms Precision Simulation Model Minakov s Formulation Equations of Motion in Minakov s Form Boundary Conditions

7 CONTENTS Motion of the Center of Mass Quasi-Static Tension Simulation Approach Resonant Excitation of Oscillations Non-Gravitational Perturbations Method of Computation Aerodynamic Forces Electrodynamic Forces Solar Radiation Pressure Thermal Expansion of the Tether Creep in the Tether Tether Mass Loss Estimation and Control Approaches Conclusions LISTENING TO THE ECHOES OF THE PAST SUBMILLIMETER PROBE OF THE EVOLUTION OF COSMIC STRUCTURE Nomenclature Observatories in Space Tethered Synthetic Aperture Interferometer Diamond Shape Configurations Symmetry and Dynamic Balance Synthetic Aperture Coverage Dynamic Model Equations of Motion Gravitational and Non-Gravitational Forces Stationary Motions Quasi-Rigid Motions Dynamic Symmetry and Integrals of Motion Tether Tension in Stationary Motion Periodic Motions Controlled Motions Tether Tension Control Controlling the Diamond Shape Configuration Changing the Spin Plane Residual Out-of-Plane Oscillations Variable Diamond Shape with Fixed Tether Lengths Tether Oscillations Tether Design and Thermal Regime Longitudinal Oscillations Transverse Oscillations Torsional Oscillations

8 6 CONTENTS The Effect of Tether Oscillations on the End-Bodies Simulation Model Fast and Slow Components of Motion Difficulties of Numeric Integration Relative Motion of the Tether Calculation of Tether Tension Modal Expansion Simulation Approaches Conclusions COLONIZING THE MOON LUNAR TRANSPORTATION SYSTEMS Nomenclature The Earth-Moon Highway Lunar Space Elevator Revisited Transfer Trajectories to the Lunar Elevator Equations of Motion and Relative Equlibrium Characteristics of Tether Configurations Non-Equatorial Configurations Fail-Safe Elevator Rotating Docking Port on the Moon The Concept Dynamic Features of the Rotating Port Conclusions FLYING IN FORMATION TRIANGULAR FORMATIONS OF TETHERED SATELLITES. 359 Nomenclature Constellations, Clusters, and Formations Triangular Tethered Formations Dynamic Model Quasi-Rigid Rotation Tether Tension Symmetrical Formations Rotation and Precession Spin Stabilization Precession of the Spin Axis Conical Precession Tidal Evolution Electrodynamic Control The effect of Ampere Forces Optimal Thrust Electromagnetic Torque

9 CONTENTS Tether Oscillations Tetrahedron Formations Conclusions SETTING SAIL ELECTRODYNAMIC SAIL CONCEPT Nomenclature Large Space Structures Electrodynamic Sail Sail Dynamics and Control Orbital Motion and Quasi-Rigid Rotation Electrodynamic Thrust Electrodynamic Torque Modelling Sail Deformations Performance Characteristics Rendezvous with a Spinning Sail Conclusions References Subject Index List of Tables