《HAMILTONIAN DYNAMICS》

1.Some Preliminaries1

1.1Newton's laws of motion1

1.2 Coordinates2

1.3 Accelerated coordinate systems3

1.4 Rigid bodies4

1.5 Constraints7

1.6 Notations9

1.7 Tensor calculus12

1.8 A Cartesian coordinate system15

1.9 The deviation equation18

1.10 Killing's equation21

Problems 126

2.Lagrange Theory in Vn30

2.1Derivation of Lagrange's equations30

2.2 Further remarks on the derivation of the Lagrange equations32

2.3 Properties of the Lagrange equations36

2.4 Excess coordinates and quasi-coordinates40

2.5 Variational methods46

2.6 Kinetic foci52

Problems 253

3.Lagrange Theory in Vn+158

3.1The Lagrange equations58

3.2 Coordinate transformations61

3.3 Action waves63

3.4 Action wave-length65

3.5 The phase-function69

3.6 Interpretation of the wave-function73

Problems 376

4.Hamiltonian Theory in V2n79

4.1Hamiltonian systems79

4.2 The space V2n85

4.3 Poisson brackets86

4.4 Dirac's use of Poisson brackets93

4.5 Transformations:canonical theory95

4.6 The generating functions97

4.7 Equivalence of all conservative holonomic problems101

4.8 The unfolding theorem103

4.9 The Lagrange brackets104

4.10 Reduction to canonical form107

4.11 Physically significant V2n's110

4.12 Conformal geometry of a V2n112

Problems 4114

5.Hamiltonian Theory in V2n+2;Integral Invariants118

5.1Equations of motion in V2n+2118

5.2 The Hamilton-Jacobi equation121

5.3 A general method of integration125

5.4 Integral invariants128

5.5 Some invariants of the first and second order130

5.6 Invariants of higher order134

5.7 The variational equations138

Problems 5141

Bibliography143

Index145