DYNAMICS OF MULTIBODY SYSTEMS
CONTENTS INTRODUCTION MULTIBODY SYSTEMS REFERENCE FRAMES PARTICLE MECHANICS RIGID BODY MECHANICS DEFORMABLE BODIES CONSTRAINED MOTION COMPUTER FORMULATION AND COORDINATE SELECTION OBJECTIVES AND SCOPE OF THIS BOOK REFERENCE KINEMATICS ROTATION MATRIX PROPERTIES OF THE ROTATION MATRIX SUCCESSIVE ROTATIONS VELOCITY EQUATIONS ACCELERATIONS AND IMPORTANT IDENTITIES RODRIGUEZ PARAMETERS EULER ANGLES DIRECTION COSINES THE 4 × 4 TRANSFORMATION MATRIX RELATIONSHIP BETWEEN DIFFERENT ORIENTATION COORDINATES PROBLEMS ANALYTICAL TECHNIQUES GENERALIZED COORDINATES AND KINEMATIC CONSTRAINTS DEGREES OF FREEDOM AND GENERALIZED COORDINATE PARTITIONING VIRTUAL WORK AND GENERALIZED FORCES LAGRANGIAN DYNAMICS APPLICATION TO RIGID BODY DYNAMICS CALCULUS OF VARIATIONS EULER’S EQUATION IN THE CASE OF SEVERAL VARIABLES EQUATIONS OF MOTION OF RIGID BODY SYSTEMS NEWTON–EULER EQUATIONS CONCLUDING REMARKS MECHANICS OF DEFORMABLE BODIES KINEMATICS OF DEFORMABLE BODIES STRAIN COMPONENTS PHYSICAL INTERPRETATION OF STRAINS RIGID BODY MOTION STRESS COMPONENTS EQUATIONS OF EQUILIBRIUM CONSTITUTIVE EQUATIONS VIRTUAL WORK OF THE ELASTIC FORCES FLOATING FRAME OF REFERENCE FORMULATION KINEMATIC DESCRIPTION INERTIA OF DEFORMABLE BODIES GENERALIZED FORCES KINEMATIC CONSTRAINTS EQUATIONS OF MOTION COUPLING BETWEEN REFERENCE AND ELASTIC DISPLACEMENTS APPLICATION TO A MULTIBODY SYSTEM USE OF INDEPENDENT COORDINATES DYNAMIC EQUATIONS WITH MULTIPLIERS GENERALIZED COORDINATE PARTITIONING ORGANIZATION OF MULTIBODY COMPUTER PROGRAMS NUMERICAL ALGORITHMS FINITE-ELEMENT FORMULATION ELEMENT SHAPE FUNCTIONS REFERENCE CONDITIONS KINETIC ENERGY GENERALIZED ELASTIC FORCES CHARACTERIZATION OF PLANAR ELASTIC SYSTEMS CHARACTERIZATION OF SPATIAL ELASTIC SYSTEMS COORDINATE REDUCTION THE FLOATING FRAME OF REFERENCE AND LARGE DEFORMATION PROBLEM THE LARGE DEFORMATION PROBLEM BACKGROUND ABSOLUTE NODAL COORDINATE FORMULATION FORMULATION OF THE STIFFNESS MATRIX RELATIONSHIP TO THE FLOATING FRAME OF REFERENCE FORMULATION COORDINATE TRANSFORMATION CONSISTENT MASS FORMULATION THE VELOCITY TRANSFORMATION MATRIX LUMPED MASS FORMULATION EXTENSION OF THE METHOD COMPARISON WITH LARGE ROTATION VECTOR FORMULATION APPENDIX: LINEAR ALGEBRA MATRIX ALGEBRA EIGENVALUE ANALYSIS VECTOR SPACES CHAIN RULE OF DIFFERENTIATION PRINCIPLE OF MATHEMATICAL INDUCTION REFERENCES