A TREATISE ON DYNAMICS
CONTENTS INTRODUCTION BASIC MATHEMATICAL TOOLS LINEAR TENSOR ALGEBRA TENSOR FIELDS DIFFERENTIAL FORMS AND MULTI-VECTORS MAPPINGS OF TENSOR FIELDS BETWEEN MANIFOLDS LIE DERIVATIVE OF TENSOR FIELDS LINEAR CONNECTION AND COVARIANT DERIVATIVE SYMPLECTIC MANIFOLDS AND SYMPLECTIC CONNECTIONS CLASSICAL HAMILTONIAN MECHANICS LAGRANGE FORMALISM AND CANONICAL HAMILTONIAN FORMALISM EQUATIONS OF MOTION IN RIEMANN SPACE HAMILTONIAN REPRESENTATION OF VARIATIONAL PROBLEMS NEWTON REPRESENTATION OF VARIATIONAL PROBLEMS COORDINATE FREE FORMULATION OF HAMILTONIAN MECHANICS POISSON AND PRESYMPLECTIC MANIFOLDS TENSOR INVARIANTS OF HAMILTONIAN SYSTEMS DUAL POISSON-PRESYMPLECTIC PAIRS CLASSICAL HAMILTONIAN FLOWS ON SYMPLECTIC MANIFOLD STATISTICAL HAMILTONIAN MECHANICS CLASSICAL POISSON ALGEBRA AND CLASSICAL STATES TIME EVOLUTION OF CLASSICAL SYSTEMS REDUCTION OF POISSON STRUCTURES AND HAMILTONIAN SYSTEMS ONTO SUBMANIFOLDS GEOMETRIC REDUCTION OF POISSON BI-VECTORS REDUCTION OF HAMILTONIAN DYNAMICS CLASSICAL INTEGRABLE AND SEPARABLE HAMILTONIAN SYSTEMS INTEGRABLE HAMILTONIAN SYSTEMS LIOUVILLE INTEGRABILITY SUPERINTEGRABILITY STÄCKEL TRANSFORM CANONICAL TRANSFORMATIONS THE MODERN FORMULATION OF HAMILTON-JACOBI THEORY LINEARIZATION OF HAMILTONIAN DYNAMICS STÄCKEL SYSTEMS INVERSE JACOBI PROBLEM STÄCKEL SYSTEMS IN RIEMANNIAN GEOMETRY KILLING TENSORS AND SEPARABLE POTENTIALS BENENTI CLASS OF SEPARABLE SYSTEMS SUPERINTEGRABILITY IN BENENTI CLASS STÄCKEL TRANSFORM FOR SEPARABLE SYSTEMS RECIPROCAL EQUIVALENCE WITH BENENTI CLASS ELEMENTARY STÄCKEL TRANSFORMS IN BENENTI CLASS THE STRUCTURE OF STÄCKEL HAMILTONIANS FROM ? -CLASSES STÄCKEL TRANSFORM OF SUPERINTEGRABLE SYSTEMS CLASSICAL SEPARABILITY THEORY BI-HAMILTONIAN SEPARABILITY THEORY BI-HAMILTONIAN LIOUVILLE INTEGRABLE SYSTEMS REDUCTION OF POISSON PENCILS ONTO SYMPLECTIC LEAVES BI-SIMPLECTIC MANIFOLDS STÄCKEL SEPARABILITY ON BI-SYMPLECTIC MANIFOLDS APPLICATION OF BI-HAMILTONIAN SEPARABILITY THEORY ELLIPTIC SEPARABLE POTENTIALS BI-COFACTOR SYSTEMS NON-PERIODIC TODA LATTICE DRESSING CHAIN BI-PRESYMPLECTIC SEPARABILITY THEORY D-COMPATIBILITY OF CLOSED TWO-FORMS AND POISSON BI-VECTORS BI-PRESYMPLECTIC CHAINS BI-INVERSE-HAMILTONIAN REPRESENTATION OF STÄCKEL SYSTEMS BI-HAMILTONIAN AND BI-PRESYMPLECTIC THEORY IN R3 POISSON AND PRESYMPLECTIC STRUCTURES IN R3 BI-HAMILTONIAN AND BI-PRESYMPLECTIC CHAINS IN R3 DIRECT TRANSFORMATION FROM SEPARATION TO FLAT COORDINATES FLAT COORDINATES FOR REAL NON DEGENERATE CASE FLAT COORDINATES FOR PARTICULAR DEGENERATION STÄCKEL TRANSFORM IN FLAT COORDINATES DEFORMATION THEORY OF CLASSICAL POISSON ALGEBRAS STAR-ALGEBRAS PRELIMINARIES FOURIER TRANSFORMS STAR PRODUCTS ON R2N CANONICAL TRANSFORMATIONS OF STAR-PRODUCTS STAR PRODUCTS ON SYMPLECTIC MANIFOLDS OPERATOR REPRESENTATION OF STAR-ALGEBRAS AND RELATED ORDERINGS WEYL ORDERING FOR MOYAL PRODUCT GENERAL THEORY OF ORDERINGS QUANTUM HAMILTONIAN MECHANICS ON SYMPLECTIC MANIFOLDS GENERAL THEORY OF QUANTIZATION QUANTUM STATES TIME EVOLUTION OF QUANTUM SYSTEMS QUANTUM TRAJECTORIES IN PHASE SPACE QUANTUM FLOW QUANTUM DYNAMICS WITH CLASSICAL TRAJECTORIES PURE QUANTUM TRAJECTORIES POSITION REPRESENTATION OF QUANTUM MECHANICS OVER RIEMANNIAN CON?GURATION SPACE OPERATOR REPRESENTATION OVER RIEMANNIAN SPACE MOYAL QUANTIZATION OTHER ADMISSIBLE QUANTIZATIONS COORDINATE TRANSFORMATION ON CON?GURATION SPACE COORDINATE FREE FORMULATION QUANTIZATION OF HYDROGEN ATOM IN CURVILINEAR COORDINATES OPERATORS LINEAR, QUADRATIC AND CUBIC IN MOMENTA QUANTUM INTEGRABILITY AND STATIONARY QUANTUM SEPARABILITY SEPARABILITY FOR MINIMAL QUANTIZATION WITH NATURAL METRIC SEPARABILITY FOR MINIMAL QUANTIZATION WITH ADOPTED METRIC MINIMAL QUANTIZATION IN DIFFERENT HILBERT SPACES QUANTUM INTEGRABILITY OF STÄCKEL SYSTEMS IN VARIOUS HILBERT SPACES QUANTIZATION OF SUPERINTEGRABLE STÄCKEL SYSTEMS R-SEPARABILITY OF STÄCKEL METRICS REFERENCES