COMPUTATIONAL DYNAMICS

By D. KIVAM

CONTENTS INTRODUCTION 1 1 COMPUTATIONAL DYNAMICS 1 2 MOTION AND CONSTRAINTS 1 3 DEGREES OF FREEDOM 1 4 KINEMATIC ANALYSIS 1 5 FORCE ANALYSIS 1 6 DYNAMIC EQUATIONS AND THEIR DIFFERENT FORMS 1 7 FORWARD AND INVERSE DYNAMICS 1 8 PLANAR AND SPATIAL DYNAMICS 1 9 COMPUTER AND NUMERICAL METHODS 1 10 ORGANIZATION, SCOPE, AND NOTATIONS OF THE BOOK LINEAR ALGEBRA 2 1 MATRICES 2 2 MATRIX OPERATIONS 2 3 VECTORS 2 4 THREE-DIMENSIONAL VECTORS 2 5 SOLUTION OF ALGEBRAIC EQUATIONS 2 6 TRIANGULAR FACTORIZATION *2 7 QR DECOMPOSITION SINGULAR VALUE DECOMPOSITION / PROBLEMS / KINEMATICS MECHANICAL JOINTS / COORDINATE TRANSFORMATION / POSITION, VELOCITY, AND ACCELERATION EQUATIONS / KINEMATICS OF A POINT MOVING ON A RIGID BODY / CONSTRAINED KINEMATICS / FORMULATION OF THE JOINT CONSTRAINTS / COMPUTATIONAL METHODS IN KINEMATICS / COMPUTER IMPLEMENTATION / KINEMATIC MODELING AND ANALYSIS / CONCLUDING REMARKS / FORMS OF THE DYNAMIC EQUATIONS D’ALEMBERT’S PRINCIPLE / CONSTRAINED DYNAMICS / AUGMENTED FORMULATION / ELIMINATION OF THE DEPENDENT ACCELERATIONS / EMBEDDING TECHNIQUE / AMALGAMATED FORMULATION / OPEN AND CLOSED CHAINS / VIRTUAL WORK AND LAGRANGIAN DYNAMICS VIRTUAL DISPLACEMENTS / KINEMATIC CONSTRAINTS AND COORDINATE PARTITIONING / VIRTUAL WORK / EXAMPLES OF FORCE ELEMENTS / WORKLESS CONSTRAINTS / PRINCIPLE OF VIRTUAL WORK IN STATICS / PRINCIPLE OF VIRTUAL WORK IN DYNAMICS / LAGRANGE’S EQUATION / GIBBS–APPEL EQUATION / HAMILTONIAN FORMULATION / RELATIONSHIP BETWEEN VIRTUAL WORK AND GAUSSIAN ELIMINATION / CONSTRAINED DYNAMICS GENERALIZED INERTIA / MASS MATRIX AND CENTRIFUGAL FORCES / EQUATIONS OF MOTION / SYSTEM OF RIGID BODIES / ELIMINATION OF THE CONSTRAINT FORCES / LAGRANGE MULTIPLIERS / CONSTRAINED DYNAMIC EQUATIONS / JOINT REACTION FORCES / ELIMINATION OF LAGRANGE MULTIPLIERS / STATE SPACE REPRESENTATION / NUMERICAL INTEGRATION / DIFFERENTIAL AND ALGEBRAIC EQUATIONS / INVERSE DYNAMICS / STATIC ANALYSIS / SPATIAL DYNAMICS GENERAL DISPLACEMENT / FINITE ROTATIONS / EULER ANGLES / VELOCITY AND ACCELERATION / GENERALIZED COORDINATES / GENERALIZED INERTIA FORCES / GENERALIZED APPLIED FORCES / DYNAMIC EQUATIONS OF MOTION / NEWTON–EULER EQUATIONS / LINEAR AND ANGULAR MOMENTUM / RECURSIVE METHODS / OTHER TOPICS IN SPATIAL DYNAMICS GYROSCOPES AND EULER ANGLES / RODRIGUEZ FORMULA / EULER PARAMETERS / RODRIGUEZ PARAMETERS / QUATERNIONS / RIGID BODY CONTACT /