Modern Astrodynamics

Name: Modern Astrodynamics | Fundamentals and Perturbation Methods
Brand: Princeton University Press
Price: 160.99 EUR
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Fundamentals and Perturbation Methods

Victor R. Bond Mark C. Allman(Autor*in)

Princeton University Press

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Erschienen am 12. Januar 2021

263 Seiten

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978-0-691-22390-2 (ISBN)

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Inhalt

Cover Page
Half-title Page
Title Page
Copyright Page
Contents
Preface
I. Fundamentals
1. Background
1.1 Introduction
1.2 Notation and Units
1.3 Time
2. The Two-Body Problem
2.1 Newton's Laws
2.2 Physics of the Two-Body Problem
2.2.1 Uniform Spherical Mass Potential
2.3 Definition of an Integral
2.4 Integrals of the Two-Body Problem
2.4.1 Area Integral c
2.4.2 Energy Integral h
2.4.3 Laplacian Integral P
2.4.4 Relationship among the Integrals
2.4.5 Summary of Integrals Derived
2.4.6 Application: The Abort Problem
2.4.7 Kepler's Equation
3. Kepler's Laws
3.1 Kepler's First Law
3.2 Kepler's Second Law
3.3 Kepler's Third Law
3.3.1 Planetary Mass Determination
4. Methods of Computation
4.1 Position/Velocity in Integrals
4.2 Position/Velocity-True Anomaly
4.3 Position/Velocity-Eccentric Anomaly
4.4 Solution of Kepler's Equation
4.5 Computation of Position/Velocity
4.5.1 Algorithm No. 1: Computing Position and Velocity
4.5.2 Algorithm No. 2: Kepler's Equation-Solution
4.6 Orbital Elements
4.7 Other Orbital Element Systems
4.7.1 Delaunay Elements
4.7.2 Poincare Elements
5. The f and g Functions
5.1 f and g Functions-Development
5.2 f and g Functions-True Anomaly
5.3 f and g Functions-Eccentric Anomaly
5.3.1 Algorithm No. 3: Computation of Delta-E
5.4 f and g Functions-Universal Variable
5.4.1 Algorithm No. 4: Using Universal Variables
5.4.2 Algorithm No. 5: Kepler's Equation-Solution
5.5 f and g Functions in Time
6. Two-Point Boundary Value Problems
6.1 Introduction
6.2 Lambert's Problem
6.3 Universal Variable
6.3.1 Algorithm No. 6: Solution of Lambert's Problem
6.4 Linear Terminal Velocity Constraint
7. Applications
7.1 Interplanetary Trajectories
7.1.1 Heliocentric Phase
7.1.2 Algorithm No. 7: V-lnfinity Vectors Solution
7.1.3 Planetocentric Phase
7.1.4 Planetary Flyby (Gravity Turn)
7.2 Space Shuttle Ascent Targets
7.3 Two-Body Anytime-Deorbit Solution
7.4 Relative Motion
7.4.1 Radial Displacement
7.4.2 Varying Eccentricity
7.4.3 Periodic Motion
7.4.4 Rotation about the Q Axis
II. Perturbation Methods
8. Perturbation Theory
8.1 Introduction
8.1.1 Explanation of Perturbation Theory
8.1.2 Elementary Example-Harmonic Oscillator
8.2 Poisson's Method
8.2.1 Elementary Example-Harmonic Oscillator
8.3 Lagrange Variation of Parameters
8.3.1 Elementary Example-Harmonic Oscillator
8.4 Two-Body Integrals of Motion
8.5 Interpretation of c, e, and N
8.6 The Perturbed Two-Body Problem
8.6.1 Energy and Semi-Major Axis
8.6.2 Angular Momentum
8.6.3 Inclination
8.6.4 The Node Angle Q
8.6.5 Laplace Vector
8.7 Some Partially Solved Problems
8.7.1 Conservative Potentials
8.7.2 Oblate Planet Potential
8.7.3 Time-Dependent Potential
8.7.4 Derivatives for a Rotating Planet
8.7.5 Derivatives for Perturbation by a Third Body
8.7.6 Tethered Satellite Problem
8.7.7 Drag Problem
9. Special Perturbation Methods
9.1 Propagation Error
9.2 Regularization
9.3 Regularizing the Two-Body Problem
9.3.1 The Jacobi Integral
9.3.2 Change to the Jacobi Integral
9.3.3 The Two-Body Solution
9.3.4 Introduction of 6 and 7
9.3.5 The Significance of Sandy
9.4 Summary of the Elements
9.5 Sperling-Burdet Approach
9.5.1 Equations for the Spatial Elements
9.5.2 Equations for the Temporal Elements
9.6 Summary of the Equations
9.7 Sperling-Burdet Method-Examples
9.7.1 Oblate Earth Plus the Moon
9.7.2 Stable Libration Points
9.7.3 Continuous Radial Thrust
10. Runge-Kutta Methods
10.1 Introduction
10.2 Error Classification
10.3 Runge-Kutta Fixed Step
10.3.1 Runge-Kutta First Order
10.3.2 Runge-Kutta Second Order
10.4 Runge-Kutta Variable Step
10.4.1 The RKF1(2)
10.4.2 Algorithm No. 8: RKF4(5)
11. Types of Perturbations
11.1 Third-Body Perturbations
11.1.1 Development of the Perturbation
11.1.2 Battiris Approach
11.1.3 Derivation of f(q)
11.1.4 Case When Position is Large in Magnitude
11.2 Potential Function for a Planet
11.2.1 Case of a Satellite about the Earth
Appendixes
A. Coordinate Transformations
A.1 Rotation of Coordinate Systems
A.2 Transformation to the Two-Body System
B. Hyperbolic Motion
C. Conic Sections
D. Transfer-Angle Resolution
E. Stumpff Functions
F. Orbit Geometry
References
Index

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