""Cover ""; ""Contents ""; ""Preface ""; ""Acknowledgments ""; ""Introduction ""; ""Chapter 1 Arbitrary Measures of the Physical World ""; ""1.1 Similarity ""; ""1.2 Dimensional Similarity ""; ""1.3 Physical Equations and the 'Pi' Theorem ""; ""1.4 Applications of the Pi Theorem ""
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""1.4.1 Plane Pendulum """"1.4.2 Pipe Flow of a Fluid ""; ""1.4.3 Steady Motion of a Rigid Object in Viscous 'Fluid' ""; ""1.4.4 Diffusion and Self-Similarity ""; ""1.4.5 Ship Wave Drag ""; ""1.4.6 Adiabatic Gas Flow ""; ""1.4.7 Time-Dependent Adiabatic Flow ""
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""1.4.8 Point Explosion in a Gaseous Medium """"1.4.9 Applications in Fundamental Physics ""; ""1.4.10 Drag on a Flexible Object in Steady Motion ""; ""1.4.11 Dimensional Analysis of Mammals ""; ""1.4.12 Trees ""; ""References ""; ""Chapter 2 Lie Groups and Scaling Symmetry ""
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""2.1 The Rescaling Group """"2.1.1 Rescaling Physical Objects ""; ""2.1.2 Reconciliation with the Buckingham Pi Theorem ""; ""2.1.3 Rescaling and Self-Similarity as a Lie Algebra ""; ""2.1.4 Practical Lie Self-Similarity ""; ""2.2 Familiar Physical Examples ""