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ANALYTICAL MECHANICS of AEROSPACE SYSTEMS Hanspeter Schaub and John L. Junkins January 1, 2002 Contents Preface ix I 1 BASIC MECHANICS 1 Particle Kinematics 1.1 Particle Position Description . . . . . . . . . . . . . 1.1.1 Basic Geometry . . . . . . . . . . . . . . . . . 1.1.2 Cylindrical and Spherical Coordinate Systems 1.2 Vector Differentiation . . . . . . . . . . . . . . . . . 1.2.1 Angular Velocity Vector . . . . . . . . . . . . 1.2.2 Rotation about a Fixed Axis . . . . . . . . . 1.2.3 Transport Theorem . . . . . . . . . . . . . . 1.2.4 Particle Kinematics with Moving Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 6 8 8 10 11 15 2 Newtonian Mechanics 2.1 Newton’s Laws . . . . . . . . . . . 2.2 Single Particle Dynamics . . . . . . 2.2.1 Constant Force . . . . . . . 2.2.2 Time-Varying Force . . . . 2.2.3 Kinetic Energy . . . . . . . 2.2.4 Linear Momentum . . . . . 2.2.5 Angular Momentum . . . . 2.3 Dynamics of a System of Particles 2.3.1 Equations of Motion . . . . 2.3.2 Kinetic Energy . . . . . . . 2.3.3 Linear Momentum . . . . . 2.3.4 Angular Momentum . . . . 2.4 Dynamics of a Continuous System 2.4.1 Equations of Motion . . . . 2.4.2 Kinetic Energy . . . . . . . 2.4.3 Linear Momentum . . . . . 2.4.4 Angular Momentum . . . . 2.5 The Rocket Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 25 29 29 32 34 35 35 38 38 41 43 45 47 47 49 50 51 52 iii . .