1 Introduction ................................................. i
1.1 The growth of theories .................................. 1
1.2 The formulation and reformulation of theories ........... 4
1.3 The structure of this book .............................. 8
2 The pre-history of classical dynamics ....................... 12
2.1 Some Greek knowledge and speculation ................... 12
2.2 The growth of mathematical astronomy ................... 16
2.3 Greek dynamical theory ................................. 20
2.4 Dynamics in medieval Islam and medieval Latin Europe ... 22
Suggested reading ........................................... 23
3 The astronomical revolution ................................. 24
3.1 Copernicus ............................................. 24
3.2 Brahe and Kepler ....................................... 29
Suggested reading ........................................... 32
4 Precursors to Newtonian dynamics ............................ 33
4.1 Galileo ................................................ 33
4.2 Descartes .............................................. 36
4.3 Huyghens ............................................... 40
4.4 Other precursors of Newton ............................. 44
Suggested reading ........................................... 45
5 The Newtonian synthesis ..................................... 46
5.1 Newtonian dynamics ..................................... 46
5.2 Newtonian gravity and Newtonian cosmology .............. 53
Suggested reading ........................................... 56
6 Philosophical aspects of the Newtonian synthesis ............ 57
6.1 The metaphysics of space, time and motion .............. 57
6.2 Issues concerning explanation .......................... 64
6.3 Newton's "Rules of reasoning in philosophy" ............ 69
Suggested reading ........................................... 74
7 The history of statics ...................................... 75
Suggested reading ........................................... 79
8 The development of dynamics after Newton .................... 80
8.1 From special problems and ad-hoc methods to general
theory ................................................. 80
8.2 Three developmental streams ............................ 85
8.3 Philosophical themes in dynamics ....................... 87
9 The "Newtonian" approach after Newton ....................... 89
9.1 Kinematics, dynamics and constitutive equations ........ 89
9.2 The fundamental laws of dynamics ....................... 91
9.3 Philosophical reflections on "force" ................... 91
Suggested reading ........................................... 95
10 From virtual work to Lagrange's equation .................... 96
10.1 From virtual work to "d'Alembert's principle" .......... 96
10.2 From d'Alembert's principle to Lagrange's equation ..... 99
Suggested reading .......................................... 100
11 Extremal principles ........................................ 102
11.1 From least time to least action ....................... 102
11.2 Least action and the issue of explanatory legitimacy .. 106
Suggested reading .......................................... 109
12 Some philosophical reflections on explanation and theory ... 110
13 Conservation principles .................................... 118
13.1 Discovery, controversy and consolidation .............. 118
13.2 Symmetry and conservation ............................. 122
Suggested reading .......................................... 127
14 Hamilton's equations ....................................... 128
14.1 The Hamiltonian formalism ............................. 128
14.2 Phase space ........................................... 130
Suggested reading .......................................... 135
15 Canonical transformations, optical analogies and
algebraic structures ....................................... 137
15.1 Canonical transformations ............................. 138
15.2 Hamilton-Jacobi theory ................................ 139
15.3 Poisson brackets ...................................... 142
Suggested reading .......................................... 143
16 The search for new foundations ............................. 144
16.1 A sampler of proposals ................................ 146
16.2 Hertz's neo-Cartesianism .............................. 149
16.3 Mach's relationism .................................... 157
16.4 Further foundational reflections ...................... 161
Suggested reading .......................................... 169
17 New directions in the applications of dynamics ............. 170
17.1 From celestial mechanics to qualitative dynamics ...... 171
17.2 Chaos theory .......................................... 187
17.3 Statistical mechanics ................................. 190
17.4 New applications and explanatory projects ............. 194
Suggested reading .......................................... 199
18 Spacetime formulations of Newtonian dynamics ............... 201
18.1 Relativistic spacetimes ............................... 202
18.2 Galilean spacetime .................................... 205
18.3 Curved Galilean spacetime and Newtonian gravity ....... 207
18.4 Philosophical reflections ............................. 209
Suggested reading .......................................... 213
19 Formalization: mass and force .............................. 214
19.1 "Informal" formalization .............................. 215
19.2 "Formal" formalization: mass and force ................ 221
Suggested reading .......................................... 234
20 Relationist dynamics ....................................... 235
20.1 Machian dynamics ...................................... 235
20.2 Philosophical questions ............................... 239
Suggested reading .......................................... 244
21 Modes of explanation ....................................... 245
21.1 The variety of explanatory modes in dynamics .......... 245
21.2 Internal issues concerning analytical dynamics ........ 248
21.3 Extremal principles and the philosophy of
explanation ........................................... 253
Suggested reading .......................................... 260
22 Retrospective and conclusions .............................. 261
References ................................................. 263
Index ......................................................... 266
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