INTRODUCTION TO THE MATHEMATICS AND METHODS OF AERODYNAMICS

Le Monde En Tique

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Ouvrage 1-56347-342-9 : INTRODUCTION TO THE MATHEMATICS AND METHODS OF AERODYNAMICS
With more than 4800 copies of the previous edition in use, this best-selling, comprehensive text documents the fundamental theoretical developments in astrodynamics and space navigation that led to Man's ventures into space. It includes the essential elements of celestial mechanics, spacecraft trajectories, and space navigation, as well as the history of the underlying mathematical developments.
The material presented in the text represents a 25-year evolution in course material developed by Dr. Battin. Former students who benefited from this material include three of the astronauts who walked on the moon.
The text format offers flexibility for the user. Chapters are largely independent of each other and may be read or taught in any order, offering the opportunity to organize an undergraduate or graduate course that meets the needs of students having various levels of background and preparation. Further, the book covers more subject matter than is covered in a single course of instruction, thereby motivating students to stray from the beaten path of the classroom.
Table of Contents
Foreword
Prologue
Contents
Preface
Introduction
PART
Hypergeometric Functions and Elliptic Integrals
Hypergeometric Functions Examples of Hypergeometric Functions Gauss' Relations for Contiguous Functions Gauss' Differential Equation Bilinear Transformation Formulas Quadratic Transformation Formulas Confluent Hypergeometric Functions Continued Fraction Expansions Gauss' Continued Fraction Expansion Theorem Continued Fractions Versus Power Series Continued Fraction Solutions of the Cubic Equation Convergence of Continued Fractions Recursive Properties of the Convergents Convergence of Class I Continued Fractions Convergence of Class II Continued Fractions Equivalent Continued Fractions Evaluating Continued Fractions Walls' Method
The Bottom-Up Method Euler's Transformation The Top-Down Method Elliptic Integrals Elliptic Integral of the First Kind Landen's Transformation Gauss' Method of the Arithmetic-Geometric Mean
Elliptic Integral of the Second Kind Evaluating Complete Elliptic Integrals Jacobi's Zeta Function Some Basic Topics in Analytical Dynamics Transformation of Coordinates Euler's Theorem
The Rotation Matrix Euler Angles
Elementary Rotation Matrices Rotation of a Vector Kinematic Form of the Rotation Matrix Euler Parameters
Multiple Rotations of a Vector Relations Among the Euler Parameters Quaternions
The n-Body Problem Equations of Motion Conservation of Total Linear Momentum Conservation of Total Angular Momentum Potential Functions Conservation of Total Energy Kinematics in Rotating Coordinates The Problem of Two Bodies Equation of Relative Motion Solution by Power Series Lagrange's Fundamental Invariants Recursion Equations for the Coefficients Integrals of the Two-Body Problem Angular Momentum Vector Eccentricity Vector The Parameter and Energy Integral Equation of Orbit
Period and Mean Motion Time of Pericenter Passage Orbital Elements and Coordinate Systems The Hodograph Plane Two-Body Orbits in the Hodograph Plane The Flight-Direction Angle The Lagrangian Coefficients Preliminary Orbit Determination Orbit from Three Coplanar Positions Orbit from Three Position Vectors Approximate Orbit from Three Position Fixes Approximate Orbit from Three Range Measurements
Approximate Orbit from Three Observations Two-Body Orbits and the Initial-Value Problem Geometrical Properties Focus-Directrix Property Focal-Radii Property Orbital Tangents
Sections of a Cone Parabolic Orbits and Barker's Equation Trigonometric Solution Improved Algebraic Solution Graphical Solution Continued Fraction Solution Descartes' Method
Lagrangian Coefficients Orbital Tangents
Elliptic Orbits and Kepler's Equation Analytic Derivation of Kepler's Equation Geometric Derivation of Kepler's Equation Lagrangian Coefficients Hyperbolic Orbits and the Gudermannian The Gudermannian Transformation Geometrical Representation of H Lagrangian Coefficients Asymptotic Coordinates Universal Formulas for Conic Orbits The Universal Functions Un(X; ?) Linear Independence of Un(X; ?) Lagrangian Coefficients and Other Orbital Quantities Identities for the Universal Functions Identities Involving Compound Arguments Identities for U2n(X; ?) Identities for Un+1Un+1-m - Un+2Un-m Identities Involving the True Anomaly Difference
Continued Fractions for Universal Functions Continued Fraction Determination of U3 and U4 Continued Fraction Determination of U5 and U6 Solving Kepler's Equation Elementary Methods Graphical Methods
Inverse Linear Interpolation (Regula Falsi) Successive Substitutions Lagrange's Expansion Theorem Euler's Trigonometric Series Generalized Expansion Theorem Convergence of the Lagrange Series Fourier-Bessel Series Expansion Series Expansion of the Eccentric Anomaly Bessel Functions
Series Expansion of the True Anomaly Series Reversion and Newton's Method Series Reversion Algorithm Newton's Method
Power Series for the Generalized Anomaly X An Alternate Form of Kepler's Equation Near-Parabolic Orbits Method of Successive Approximations Motivating Gauss' Method Gauss' Method
Extending Gauss' Method Transformation of Kepler's Equation Solution of the Cubic Equation Series Representations Algorithm for the Kepler Problem Two-Body Orbital Boundary-Value Problem Terminal Velocity Vectors Minimum-Energy Orbit Locus of Velocity Vectors Parameter in Terms of Velocity-Components Ratio Parameter in Terms of Flight-Direction Angle Relation Between Velocity and Eccentricity Vectors Orbit Tangents and the Transfer-Angle Bisector Ellipse and Hyperbola Parabola
Parameter in Terms of Eccentric-Anomaly Difference
The Fundamental Ellipse The Fundamental (Minimum-Eccentricity) Ellipse Intersection of the Transfer-Angle Bisector and the Chord Parameter in Terms of Eccentricity Tangent Ellipses
A Mean Value Theorem Geometry of the Mean-Point Locus The Mean-Point Radius Elegant Expressions for the Mean-Point Radii Parameter in Terms of Mean-Point Radius Locus of the Vacant Focus Elliptic Orbits
Hyperbolic Orbits
Parameter in Terms of Semimajor Axis Lambert's Theorem
Euler's Equation for Parabolic Orbits Lagrange's Equation for Elliptic Orbits The Orbital Parameter Transforming the Boundary-Value Problem Transforming to a Rectilinear Ellipse Transformingto a Rectilinear Hyperbola Terminal Velocity Vector Diagrams Elliptic Orbits
Parabolic Orbit
Hyperbolic Orbits
Boundary Conditions at Infinity Solving Lambert's Problem Formulations of the Transfer-Time Equation Lagrange's Equation Gauss' Equation
Combined Equations Multiple-Revolution Transfer Orbits The Velocity Vector The Q Function
Improving the Convergence Continued Fraction Representation Derivative Formulas Gauss' Method
The Classical Equations of Gauss Solving Gauss' Equations Solving Gauss' Cubic Equation An Alternate Geometric Transformation Transforming the Mean Point to an Apse Relating h and ? to the Original Orbit Improving Gauss' Method Removing the Singularity Computing l, m, and the Orbital Elements Improving the Convergence Transforming the Function ?(x) Solving the Cubic
Comparing the Two Methods Behaviour Near the Singularity Appendices A Mathematical Progressions A.1 Arithmetic Progression A.2 Geometric Progression A.3 Harmonic Progression B Vector and Matrix Algebra B.1 Vector Algebra B.2 Matrix Algebra C Power Series Manipulations D Linear Algebraic Systems E Conic Sections
F Tschebycheff Approximations F.1 Tschebycheff Polynomials F.2 Economization of Power Series G Plane Trigonometry PART
Non-Keplerian Motion Lagrange's Solution of the Three-Body Problem Equilateral Triangle Solution Straight Line Solutions Conic Section Solutions The Restricted Problem of Three Bodies Jacobi's Integral
Rectilinear Oscillation of an Infinitesimal Mass Surfaces of Zero Relative Velocity Lagrangian Points
Stability of the Lagrangian Points The Equilateral Libration Points The Collinear Libration Points The Disturbing Function Explicit Calculation of the Disturbing Acceleration Expansion of the Disturbing Function Jacobi's Expansion and Rodrigues' Formula Legendre Polynomials The Sphere of Influence The Canonical Coordinates of Jacobi Potential of Distributed Mass MacCullagh's Approximation Expansion as a Series of Legendre Functions Spacecraft Motion Under Continuous Thrust Constant Radial Acceleration Transforming the Integral to Normal Form Constant Tangential Acceleration Patched-Conic Orbits and Perturbation Methods Approach Trajectories Near a Target Planet Close Pass of a Target Planet Tisserand's Criterion Surface Impact at a Target Planet Interplanetary Orbits Planetary Flyby Orbits Impulse Control of Flyby Altitude Examples of Free-Return, Flyby Orbits

Auteur : BATTIN
Editeur : AMERICAN INSTITUTE
Nombre de pages : 797
Date de publication : 05 1999

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