THE ADVANCED PART OF A TREATISE ON THE DYNAMICS OF A SYSTEM OF RIGID BODIES
CONTENTS INTRODUCTION AIMS AND OBJECTIVES ATMOSPHERIC AND SPACE FLIGHT MODELING AND SIMULATION SUMMARY ATTITUDE AND KINEMATICS OF COORDINATE FRAMES BASIC DE?NITIONS AND VECTOR OPERATIONS COORDINATE SYSTEMS AND ROTATION MATRIX EULER AXIS AND PRINCIPAL ANGLE EULER ANGLES EULER SYMMETRIC PARAMETERS (QUATERNION) RODRIGUES PARAMETERS (GIBBS VECTOR) MODI?ED RODRIGUES PARAMETERS ATTITUDE KINEMATICS 2 10 SUMMARY EXERCISES PLANETARY FORM AND GRAVITY NEWTON’S LAW OF GRAVITATION GRAVITY OF AN AXISYMMETRIC PLANET RADIUS OF A NONSPHERICAL PLANET GRAVITATIONAL ANOMALIES TRANSLATIONAL MOTION OF AEROSPACE VEHICLES PARTICLE AND BODY PARTICLE KINEMATICS IN A MOVING FRAME NEWTON’S LAWS OF MOTION VARIABLE MASS BODIES ROTATION AND TRANSLATION OF A BODY ENERGY AND ANGULAR MOMENTUM THE N -BODY PROBLEM THE TWO-BODY PROBLEM GEOMETRY OF TWO-BODY TRAJECTORIES LAGRANGE’S COE?CIENTS KEPLER’S EQUATION FOR ELLIPTICAL ORBIT POSITION AND VELOCITY IN A HYPERBOLIC TRAJECTORY PARABOLIC ESCAPE TRAJECTORY ORBITAL MECHANICS CELESTIAL FRAME AND ORBITAL ELEMENTS ORBIT DETERMINATION SPHERICAL CELESTIAL COORDINATES AND LOCAL HORIZON PLANET FIXED FRAME SINGLE IMPULSE ORBITAL MANEUVERS MULTI-IMPULSE ORBITAL TRANSFER RELATIVE MOTION IN ORBIT LAMBERT’S PROBLEM PERTURBED ORBITS PERTURBING ACCELERATION E?ECTS OF PLANETARY OBLATENESS SUN SYNCHRONOUS ORBITS MOLNIYA ORBITS E?ECTS OF ATMOSPHERIC DRAG THIRD-BODY PERTURBATION AND INTERPLANETARY FLIGHT SPHERE OF IN?UENCE AND PATCHED CONICS NUMERICAL SOLUTION TO THE PERTURBED PROBLEM THE THREE-BODY PROBLEM EQUATIONS OF MOTION LAGRANGE’S SOLUTION RESTRICTED THREE-BODY PROBLEM LAGRANGIAN POINTS AND THEIR STABILITY JACOBI’S INTEGRAL NUMERICAL SOLUTION OF THE RESTRICTED PROBLEM ROCKET PROPULSION THE ROCKET ENGINE THE ROCKET EQUATION AND STAGING THE SINGLE-STAGE ROCKET THE MULTI-STAGE ROCKET PARALLEL STAGING MISSION TRADE-O? OPTIMAL ROCKETS OPTIMAL TWO-STAGE ROCKET OPTIMAL THREE-STAGE ROCKET PLANETARY ATMOSPHERE HYDROSTATIC EQUILIBRIUM STANDARD ATMOSPHERE EXPONENTIAL MODEL FOR PLANETARY ATMOSPHERES ELEMENTS OF AERODYNAMICS 10 1 AIMS AND OBJECTIVES 10 2 BASIC CONCEPTS 10 2 1 AERODYNAMIC FORCE AND MOMENT 10 3 FLUID DYNAMICS 10 3 1 FLOW REGIMES 10 3 2 CONTINUUM FLOW 10 3 3 CONTINUUM VISCOUS FLOW AND THE BOUNDARY LAYER 10 3 4 CONTINUUM COMPRESSIBLE FLOW 10 3 5 RARE?ED FLOW 10 4 FORCE AND MOMENT COE?CIENTS 10 5 SUMMARY AIRBREATHING PROPULSION 11 1 AIMS AND OBJECTIVES 11 2 IDEAL MOMENTUM THEORY 11 3 PROPELLER ENGINES 11 4 JET ENGINES 11 4 1 RAMJET ENGINES 11 4 2 TURBOJET AND TURBOFAN ENGINES 11 5 SUMMARY ATMOSPHERIC AND TRANSATMOSPHERIC TRAJECTORIES 12 1 AIMS AND OBJECTIVES 12 2 EQUATIONS OF MOTION 12 3 AIRPLANE FLIGHT PATHS 12 3 1 LONG-RANGE CRUISING FLIGHT 12 3 2 E?ECT OF A STEADY WIND ON AN AIRPLANE FLIGHT 12 3 3 TAKE-O?MANEUVER 12 3 4 ACCELERATED CLIMB 12 3 5 MANEUVERS AND SUPERMANEUVERS 12 4 ENTRY TRAJECTORIES 12 4 1 BALLISTIC ENTRY 12 4 2 MANEUVERING ENTRY 12 5 ROCKET ASCENT TRAJECTORIES 12 6 SUMMARY ATTITUDE DYNAMICS 13 1 AIMS AND OBJECTIVES 13 2 EULER EQUATIONS OF ROTATIONAL MOTION 13 3 ROTATIONAL KINETIC ENERGY 13 4 PRINCIPAL BODY FRAME 13 5 TORQUE-FREE ROTATION OF SPACECRAFT 13 5 1 AXISYMMETRIC SPACECRAFT 13 5 2 ASYMMETRIC SPACECRAFT 13 6 SPACECRAFT WITH ATTITUDE THRUSTERS 13 6 1 SINGLE-AXIS IMPULSIVE ROTATION 13 6 2 ATTITUDE MANEUVERS OF SPIN-STABILIZED SPACECRAFT 13 6 3 ASYMMETRIC SPACECRAFT MANEUVERS BY ATTITUDE THRUSTERS 13 7 SPACECRAFT WITH ROTORS 13 7 1 VARIABLE-SPEED CONTROL MOMENT GYROSCOPE 13 7 2 DUAL-SPIN SPACECRAFT 13 7 3 GRAVITY GRADIENT SPACECRAFT 13 8 ATTITUDE MOTION IN ATMOSPHERIC FLIGHT 13 8 1 EQUATIONS OF MOTION WITH SMALL DISTURBANCE 13 8 2 STABILITY DERIVATIVES AND DE-COUPLED DYNAMICS 13 8 3 LONGITUDINAL DYNAMICS 13 8 4 AIRPLANE LONGITUDINAL MODES 13 8 5 LATERAL DYNAMICS 13 8 6 AIRPLANE LATERAL MODES 13 8 7 ROTATIONAL MOTION OF A LAUNCH VEHICLE 13 8 8 INERTIA COUPLED DYNAMICS 13 9 SUMMARY ATTITUDE CONTROL SYSTEMS 14 1 AIMS AND OBJECTIVES 14 2 INTRODUCTION 14 3 LINEAR SYSTEMS 14 3 1 TIME-INVARIANT, LINEAR SYSTEMS 14 3 2 LINEAR STABILITY CRITERIA 14 3 3 TRANSFER MATRIX AND SECOND-ORDER SYSTEMS 14 4 BASIC CLOSED-LOOP SYSTEMS 14 5 IMPLEMENTATION OF CONTROL SYSTEM ELEMENTS 14 5 1 GYROSCOPIC SENSORS 14 6 SINGLE-AXIS, CLOSED-LOOP ATTITUDE CONTROL 14 6 1 CONTROL OF SINGLE-AXIS SPACECRAFT MANEUVERS 14 6 2 ROLL CONTROL OF AIRCRAFT AND MISSILES 14 7 MULTI-AXIS CLOSED-LOOP ATTITUDE CONTROL 14 7 1 ATTITUDE STABILIZATION OF A LAUNCH VEHICLE 14 7 2 REACTION WHEEL AND MAGNETIC DENUTATION OF GRAVITY GRADIENT SPACECRAFT 14 7 3 CONTROL OF AIRCRAFT AND MISSILES WITH INERTIA COUPLING 14 8 SUMMARY ADVANCED MODELING AND SIMULATION CONCEPTS 15 1 AIMS AND OBJECTIVES 15 2 SIX-DEGREE-OF-FREEDOM SIMULATION 15 2 1 WING-ROCK MOTION OF A FIGHTER AIRPLANE 15 2 2 TRAJECTORY AND ATTITUDE OF A BALLISTIC ENTRY VEHICLE 15 3 STRUCTURAL DYNAMICS 15 4 UNSTEADY AERODYNAMICS AND AEROELASTICITY 15 5 PROPELLANT SLOSH DYNAMICS 15 6 SUMMARY A NUMERICAL INTEGRATION OF ORDINARY DI?ERENTIAL EQUATIONS A 1 FIXED-STEP RUNGE–KUTTA ALGORITHMS A 2 VARIABLE-STEP RUNGE–KUTTA ALGORITHMS A 3 RUNGE–KUTTA–NYSTR¨OM ALGORITHMS ANSWERS TO SELECTED EXERCISES REFERENCES