RIGID BODY DYNAMICS ALGORITHMS

By JESSICA PEREZ

CONTENTS INTRODUCTION DYNAMICS ALGORITHMS SPATIAL VECTORS UNITS AND NOTATION READERS’ GUIDE FURTHER READING SPATIAL VECTOR ALGEBRA MATHEMATICAL PRELIMINARIES SPATIAL VELOCITY SPATIAL FORCE PL¨UCKER NOTATION LINE VECTORS AND FREE VECTORS SCALAR PRODUCT USING SPATIAL VECTORS COORDINATE TRANSFORMS SPATIAL CROSS PRODUCTS 2 10 DI?ERENTIATION 2 11 ACCELERATION 2 12 MOMENTUM 2 13 INERTIA 2 14 EQUATION OF MOTION 2 15 INVERSE INERTIA 2 16 PLANAR VECTORS 2 17 FURTHER READING DYNAMICS OF RIGID BODY SYSTEMS EQUATIONS OF MOTION CONSTRUCTING EQUATIONS OF MOTION VECTOR SUBSPACES CLASSI?CATION OF CONSTRAINTS JOINT CONSTRAINTS DYNAMICS OF A CONSTRAINED RIGID BODY DYNAMICS OF A MULTIBODY SYSTEM MODELLING RIGID BODY SYSTEMS CONNECTIVITY GEOMETRY DENAVIT-HARTENBERG PARAMETERS JOINT MODELS SPHERICAL MOTION A COMPLETE SYSTEM MODEL INVERSE DYNAMICS ALGORITHM COMPLEXITY RECURRENCE RELATIONS THE RECURSIVE NEWTON-EULER ALGORITHM THE ORIGINAL VERSION ADDITIONAL NOTES FORWARD DYNAMICS — INERTIA MATRIX METHODS THE JOINT-SPACE INERTIA MATRIX THE COMPOSITE-RIGID-BODY ALGORITHM A PHYSICAL INTERPRETATION BRANCH-INDUCED SPARSITY SPARSE FACTORIZATION ALGORITHMS FORWARD DYNAMICS — PROPAGATION METHODS ARTICULATED-BODY INERTIA CALCULATING ARTICULATED-BODY INERTIAS THE ARTICULATED-BODY ALGORITHM ALTERNATIVE ASSEMBLY FORMULAE MULTIPLE HANDLES CLOSED LOOP SYSTEMS LOOP CONSTRAINT EQUATIONS CONSTRAINT STABILIZATION LOOP JOINT FORCES SOLVING THE EQUATIONS OF MOTION ALGORITHM FOR C ?? A ALGORITHM FOR K AND K ALGORITHM FOR G AND G EXPLOITING SPARSITY IN K AND G 8 10 SOME PROPERTIES OF CLOSED-LOOP SYSTEMS 8 11 LOOP CLOSURE FUNCTIONS 8 12 INVERSE DYNAMICS 8 13 SPARSE MATRIX METHOD HYBRID DYNAMICS AND OTHER TOPICS HYBRID DYNAMICS ARTICULATED-BODY HYBRID DYNAMICS FLOATING BASES FLOATING-BASE FORWARD DYNAMICS FLOATING-BASE INVERSE DYNAMICS GEARS DYNAMIC EQUIVALENCE 10 ACCURACY AND E?CIENCY 10 1 SOURCES OF ERROR 10 2 THE SENSITIVITY PROBLEM 10 3 E?CIENCY 10 4 SYMBOLIC SIMPLI?CATION 11 CONTACT AND IMPACT 11 1 SINGLE POINT CONTACT 11 2 MULTIPLE POINT CONTACTS 11 3 A RIGID-BODY SYSTEM WITH CONTACTS 11 4 INEQUALITY CONSTRAINTS 11 5 SOLVING CONTACT EQUATIONS 11 6 CONTACT GEOMETRY 11 7 IMPULSIVE DYNAMICS 11 8 SOFT CONTACT 11 9 FURTHER READING