AN ELEMENTARY TREATISE ON THE DYNAMICS OF A SYSTEM OF RIGID BODIES
1 Preliminary Remarks on Vectors and Matrices 1 11 Vector 1 111 Definition 1 112 Operations 3 12 Matrix 8 121 Definition 8 122 Operations 10 2 Kinematics 19 21 Coordinate Frames 19 22 Position and Orientation 22 221 Vector Notations 23 222 Orientation 25 223 Position 28 23 Velocity 34 231 Linear Velocity 34 232 Angular Velocity 36 233 Relation Between Linear and Angular Velocities 40 24 Acceleration 42 3 Dynamics 61 31 Inertial Properties 61 311 Definitions 61 312 Theorems and Rules 68 32 Momentum 73 321 Linear Momentum 74 322 Angular Momentum 74 33 Force, Moment of Force, Torque,Work, and Power 80 34 Impulse,Work, and Power 82 35 Kinetic Energy, Potential Energy, andMechanical Energy Conservation 84 36 Equations of Motion 90 361 Newton–Euler Formulation 91 362 D’Alembert’s Principle 110 363 Lagrange Equations 117 4 Case Studies 131 41 Two-Link Planar Robotic Arm 131 42 Human Body Doing Twisting Somersaults 138 43 Bicycle Balance 143 References 151