Missile Guidance and Control Systems

TLDR: In this paper, the authors present a mathematical model for the trajectory of a single-stage ballistic missile, which is based on the D'Alembert's principle of transformation properties of Vectors.

Abstract: Contents 1 Introduction References 2 The Generalized Missile Equations of Motion 2.1 Coordinate Systems 2.1.1 Transformation Properties of Vectors 2.1.2 Linear Vector Functions 2.1.3 Tensors 2.1.4 Coordinate Transformations 2.2 Rigid-Body Equations of Motion 2.3 D'Alembert's Principle 2.4 Lagrange's Equations for Rotating Coordinate Systems References 3 Aerodynamic Forces and Coefficients 3.1 Aerodynamic Forces Relative to the Wind Axis System 3.2 Aerodynamic Moment Representation 3.2.1 Airframe Characteristics and Criteria 3.3 System Design and Missile Mathematical Model 3.3.1 System Design 3.3.2 The Missile Mathematical Model 3.4 The Missile Guidance System Model 3.4.1 The Missile Seeker Subsystem 3.4.2 Missile Noise Inputs 3.4.3 Radar Target Tracking Signal 3.4.4 Infrared Tracking Systems 3.5 Autopilots 3.5.1 Control Surfaces and Actuators 3.6 English Bias References 4 Tactical Missile Guidance Laws 4.1 Introduction 4.2 Tactical Guidance Intercept Techniques 4.2.1 Homing Guidance 4.2.2 Command and Other Types of Guidance 4.3 Missile Equations of Motion 4.4 Derivation of the Fundamental Guidance Equations 4.5 Proportional Navigation 4.6 Augmented Proportional Navigation 4.7 Three-Dimensional Proportional Navigation 4.8 Application of Optimal Control of Linear Feedback Systems with Quadratic Performance Criteria in Missile Guidance 4.8.1 Introduction 4.8.2 Optimal Filtering 4.8.3 Optimal Control of Linear Feedback Systems with Quadratic Performance Criteria 4.8.4 Optimal Control for Intercept Guidance 4.9 End Game References 5 Weapon Delivery Systems 5.1 Introduction 5.2 Definitions and Acronyms Used in Weapon Delivery 5.2.1 Definitions 5.2.2 Acronyms 5.3 Weapon Delivery Requirements 5.3.1 Tactics and Maneuvers 5.3.2 Aircraft Sensors 5.4 The Navigation/Weapon Delivery System 5.4.1 The Fire Control Computer 5.5 Factors In.uencing Weapon Delivery Accuracy 5.5.1 Error Sensitivities 5.5.2 Aircraft Delivery Modes 5.6 Unguided Weapons 5.6.1 Types of Weapon Delivery 5.6.2 Unguided Free-Fall Weapon Delivery 5.6.3 Release Point Computation for Unguided Bombs 5.7 The Bombing Problem 5.7.1 Conversion of Ground Plane Miss Distance into Aiming Plane Miss Distance 5.7.2 Multiple Impacts 5.7.3 Relationship Among REP, DEP, and CEP 5.8 Equations of Motion 5.9 Covariance Analysis 5.10 Three-Degree-of-Freedom Trajectory Equations and Error Analysis 5.10.1 Error Analysis 5.11 Guided Weapons 5.12 Integrated Flight Control in Weapon Delivery 5.12.1 Situational Awareness/Situation Assessment (SA/SA) 5.12.2 Weapon Delivery Targeting Systems 5.13 Air-to-Ground Attack Component 5.14 Bomb Steering 5.15 Earth Curvature 5.16 Missile Launch Envelope 5.17 Mathematical Considerations Pertaining to the Accuracy of Weapon Delivery Computations References 6 Strategic Missiles 6.1 Introduction 6.2 The Two-Body Problem 6.3 Lambert's Theorem 6.4 First-Order Motion of a Ballistic Missile 6.4.1 Application of the Newtonian Inverse-Square Field Solution to Ballistic Missile Flight 6.4.2 The Spherical Hit Equation 6.4.3 Ballistic Error Coef.cients 6.4.4 Effect of the Rotation of the Earth 6.5 The Correlated Velocity and Velocity-to-Be-Gained Concepts 6.5.1 Correlated Velocity 6.5.2 Velocity-to-Be-Gained 6.5.3 The Missile Control System 6.5.4 Control During the Atmospheric Phase 6.5.5 Guidance Techniques 6.6 Derivation of the Force Equation for Ballistic Missiles 6.6.1 Equations of Motion 6.6.2 Missile Dynamics 6.7 Atmospheric Reentry 6.8 Missile Flight Model 6.9 Ballistic Missile Intercept 6.9.1 Introduction 6.9.2 Missile Tracking Equations of Motion References 7 Cruise Missiles 7.1 Introduction 7.2 System Description<7.2.1 System Functional Operation and Requirements 7.2.2 Missile Navigation System Description 7.3 Cruise Missile Navigation System Error Analysis 7.3.1 Navigation Coordinate System 7.4 Terrain Contour Matching (TERCOM) 7.4.1 Introduction 7.4.2 De.nitions 7.4.3 The Terrain-Contour Matching (TERCOM) Concept 7.4.4 Data Correlation Techniques 7.4.5 Terrain Roughness Characteristics 7.4.6 TERCOM System Error Sources 7.4.7 TERCOM Position Updating 7.5 The NAVSTAR/GPS Navigation System 7.5.1 GPS/INS Integration References A Fundamental Constants B Glossary of Terms C List of Acronyms D The Standard Atmospheric Model References E Missile Classi.cation F Past and Present Tactical/Strategic Missile Systems F.1 Historical Background F.2 Unpowered Precision-Guided Munitions (PGM) References G Properties of Conics G.1 Preliminaries G.2 General Conic Trajectories References H Radar Frequency Bands I Selected Conversion Factors Index