THE ADVANCED PART: TREATISE ON THE WHOLE SUBJECT OF DYNAMICS OF A SYSTEM OF RIGID BODIES

By CHARLES GONZALEZ

CONTENTS PRELIMINARIES ON VECTORS, MATRICES, COMPLEX NUMBERS AND QUATERNIONS VECTORS DE?NITION OPERATIONS MATRICES COMPLEX NUMBERS QUATERNIONS SOME DE?NITIONS AND RELATIONS SPECIAL VECTORS, MATRICES, AND TERMS ORIENTATION AND POSITION REPRESENTATION COORDINATE FRAMES OBSERVATION FRAME, DESCRIPTION FRAME, AND VECTOR NOTATION ORIENTATION ROTATION MATRIX [2,8] EQUIVALENT/EFFECTIVE AXIS AND ANGLE EXPONENTIAL COORDINATES ACTIVE/PASSIVE INTERPRETATIONS OF ROTATION MATRIX AND ORIENTATION FROM SUCCESSIVE ROTATIONS EULER ANGLES RPY ANGLES QUATERNION OF ROTATION CAYLEY–KLEIN MATRIX POSITION POSITION OF A RIGID BODY AND POSITION OF A POINT PASSIVE AND ACTIVE REPRESENTATION OF POSITION EXAMPLES VELOCITY AND ACCELERATION ANGULAR VELOCITY ANGULAR VELOCITY DERIVED FROM ROTATION MATRIX ANGULAR VELOCITY AND THE TIME DERIVATIVE OF A VECTOR FIXED IN THE BODY FRAME ANGULAR VELOCITY DERIVED FROM EULER ANGLES AND RPY ANGLES ANGULAR VELOCITY DERIVED FROM EQUIVALENT/EFFECTIVE AXIS AND ANGLE ANGULAR VELOCITY DERIVED FROM QUATERNION OF ROTATION ANGULAR VELOCITY FOR SUCCESSIVE ROTATIONS LINEAR VELOCITY ACCELERATION ANGULAR ACCELERATION LINEAR ACCELERATION DYNAMICS INERTIAL PROPERTIES INERTIAL PROPERTIES FOR LINEAR MOTION INERTIAL PROPERTIES FOR ANGULAR MOTION INERTIA ELLIPSOID EXAMPLE THEOREMS AND RULES MOMENTUM LINEAR MOMENTUM ANGULAR MOMENTUM FORCE, MOMENT OF FORCE, AND TORQUE IMPULSE, WORK AND POWER MECHANICAL ENERGY KINETIC ENERGY POTENTIAL ENERGY EQUATIONS OF MOTION NEWTON–EULER FORMULATION D’ALEMBERT’S PRINCIPLE LAGRANGE’S EQUATIONS CASE STUDIES TWO-LINK PLANAR ROBOTIC ARM THE HUMAN BODY DOING TWISTING SOMERSAULTS BICYCLE BALANCE REFERENCES