endobj endobj endobj 211 0 obj 185 0 obj endobj
180 0 obj 80 0 obj (Space Translation Symmetry) << /S /GoTo /D (section.2.2) >> 21 0 obj (Relativistic Particle in an Electromagnetic Field) (Conservation of Energy) /Contents 196 0 R 117 0 obj endobj << /S /GoTo /D (section.3.7) >> 125 0 obj /D [203 0 R /XYZ 85.457 721 null] (Disk Pulled by Falling Mass) endobj 57 0 obj 205 0 obj endobj >> 129 0 obj <<
(Comments) << /S /GoTo /D (subsection.2.3.2) >> endobj /D [209 0 R /XYZ 71 721 null] << /S /GoTo /D (section.4.3) >> << /S /GoTo /D (section.1.1) >> stream 164 0 obj << /S /GoTo /D (subsection.4.4.2) >> 105 0 obj >>
(The Principle of Least Action and Geodesics) << /S /GoTo /D (chapter.3) >> 4 0 obj 197 0 obj endobj 
(The Ubiquity of Geodesic Motion) << /S /GoTo /D (subsection.2.2.3) >> << /S /GoTo /D (section.3.4) >> endobj /Font << /F52 206 0 R /F40 200 0 R /F26 207 0 R >> (Hamilton's Equations from the Principle of Least Action) 113 0 obj (Wave Equations) (Hamilton's Equations) 192 0 obj 45 0 obj 121 0 obj 124 0 obj /D [194 0 R /XYZ 86.457 662.536 null] xu=O0m K^[>(C.( ^ endobj (Another Lagrangian for Relativistic Electrodynamics) << 37 0 obj /Filter /FlateDecode >> endobj endstream /Length 166 (Noether's Theorem) endobj /Filter /FlateDecode endobj endobj 189 0 obj (Example: General Relativistic Particle in an E-M Potential) endobj /Type /Page x3PHW0Ppr << /S /GoTo /D (subsection.2.3.1) >> 202 0 obj /ProcSet [ /PDF /Text ] (The Euler\205Lagrange Equations) 25 0 obj 12 0 obj endobj 89 0 obj endobj 184 0 obj << << /S /GoTo /D (chapter.1) >> 48 0 obj 109 0 obj << >> endobj endobj >> >> /Font << /F52 206 0 R >> endobj
endobj >> 169 0 obj endobj 214 0 obj 177 0 obj (Prehistory of the Lagrangian Approach) % xU0I8?ZHe TH "Nl+QGQ4r38K*+El.VX* i+"T\91~BA"vN}):>'!xHtd=2&?t> 85 0 obj endobj << /S /GoTo /D (subsection.4.2.3) >> 101 0 obj >> /D [194 0 R /XYZ 85.457 721 null] /Parent 201 0 R 168 0 obj endobj 24 0 obj endobj 53 0 obj << /S /GoTo /D (section.2.3) >> stream (The Hamilton-Jacobi Equations) endobj 97 0 obj 144 0 obj endobj endobj >> 145 0 obj << /S /GoTo /D (subsection.2.2.2) >> (The Atwood Machine) endobj
<< /S /GoTo /D (section.3.8) >>
128 0 obj << /S /GoTo /D (section.3.5) >> 209 0 obj 96 0 obj (Noether's Theorem) /Type /Page endobj 188 0 obj 210 0 obj << /S /GoTo /D (subsection.3.11.1) >> << /S /GoTo /D (subsection.2.2.1) >> endobj << /S /GoTo /D (chapter.2) >> /Length 67 << /S /GoTo /D (section.3.11) >> !) endobj << endobj (Gauge Symmetries) 204 0 obj (Symmetries) 116 0 obj << /S /GoTo /D (subsection.1.2.2) >> 161 0 obj endobj 153 0 obj endobj (Regular and Strongly Regular Lagrangians) endobj endobj 104 0 obj 93 0 obj (Lagrangian and Newtonian Approaches) endobj << (From Lagrangians to Hamiltonians) endobj 9 0 obj endobj 76 0 obj endobj endobj endobj /ProcSet [ /PDF /Text ] 81 0 obj (Lagrangian versus Hamiltonian Approaches) (Waves versus Particles\204The Hamilton-Jacobi Equations) 148 0 obj xXKWL"lKoUl9JT9`8!JrBZ~qE\HF?n 7g=9wf"K\M03EP=$on$afG2=5bv. 196 0 obj (Conserved Quantities from Symmetries) << /S /GoTo /D (section.2.1) >>
141 0 obj
endobj endobj 208 0 obj (Relativistic Hamiltonian) endobj
endobj 36 0 obj << /S /GoTo /D (section.3.6) >>
stream (Example: A Regular but not Strongly Regular Lagrangian) >> << /S /GoTo /D (subsection.1.1.1) >> /Contents 210 0 R (Example: A Particle in a Riemannian Manifold with Potential V\(q\)) endobj endobj endobj << /S /GoTo /D (subsection.4.2.4) >> endobj 133 0 obj (Hamilton and Euler\205Lagrange) 29 0 obj endobj << /S /GoTo /D (subsection.4.2.2) >> endobj endobj endobj endobj (A Charged Particle on a Curved Spacetime) 13 0 obj endobj u3)t}s/H 7B Gw=ojRN9An F|. endobj (Time Translation Symmetry) 65 0 obj >> endobj 68 0 obj 176 0 obj 17 0 obj 1 0 obj << /S /GoTo /D [194 0 R /FitH] >> endobj endobj 100 0 obj endobj 73 0 obj endobj 140 0 obj /Length 240 /Resources 208 0 R (From Newtonian to Lagrangian Mechanics) 72 0 obj endobj endobj endobj 165 0 obj 92 0 obj /Length 2529 endobj endobj 156 0 obj endobj /Filter /FlateDecode 64 0 obj endobj 136 0 obj << /S /GoTo /D (subsection.2.2.4) >> (Bead on a Rotating Rod) << /S /GoTo /D (subsection.4.4.1) >> << /S /GoTo /D (section.4.4) >> << /S /GoTo /D (subsection.3.5.1) >> (Examples) << /S /GoTo /D (subsection.1.2.4) >> << /S /GoTo /D (subsection.3.4.1) >> 41 0 obj endobj endobj endobj (Jacobi and Least Time vs Least Action) << /S /GoTo /D (subsection.2.3.3) >> endobj 195 0 obj 194 0 obj 40 0 obj 61 0 obj << /S /GoTo /D (section.3.10) >> 52 0 obj stream endobj 108 0 obj
endobj 28 0 obj endobj 160 0 obj (Time Translation) 198 0 obj << endobj endobj 9sdY#%msL\ho4v( #.4wZ}7}*['2QejVZ\u{q9qoY!j3VNF`-~q,iv513'{P\^[ << /S /GoTo /D (section.3.9) >> << /S /GoTo /D (section.4.1) >> endobj 172 0 obj endobj 32 0 obj 5 0 obj /MediaBox [0 0 612 792] 193 0 obj 157 0 obj 181 0 obj endobj endobj << 20 0 obj << /S /GoTo /D (subsection.4.3.1) >> 120 0 obj endobj endobj 132 0 obj << /S /GoTo /D (chapter.4) >> 44 0 obj 137 0 obj 112 0 obj /MediaBox [0 0 612 792] (The Hamiltonian Approach) << /S /GoTo /D (subsection.4.3.2) >> (Lagrangian Mechanics) 8 0 obj << /S /GoTo /D (section.1.2) >> >> endobj endobj << endobj << /S /GoTo /D (section.3.2) >> endobj 173 0 obj endobj 152 0 obj 149 0 obj 77 0 obj endobj << /S /GoTo /D (subsection.3.11.2) >> (Virtual Work) fzFf endobj << /S /GoTo /D (section.3.3) >> 88 0 obj 69 0 obj endobj << endobj endobj endobj << /S /GoTo /D (section.4.2) >> (Example: Free General Relativistic Particle with Reparameterization Invariance) 49 0 obj 33 0 obj /Parent 201 0 R
z (From Virtual Work to the Principle of Least Action) endobj (The Free Particle in General Relativity) 60 0 obj
(Lagrangian for a String) (The Principle of Least Time) endobj %PDF-1.5 >> /Filter /FlateDecode endobj << /S /GoTo /D (subsection.4.2.1) >> (The Principle of Minimum Energy) endobj (Rotational Symmetry) << endobj 56 0 obj
endobj (Free Particle in Special Relativity) << /S /GoTo /D (section.3.1) >> << /S /GoTo /D (subsection.1.2.1) >> endobj 84 0 obj /Font << /F39 199 0 R /F40 200 0 R >> endobj 16 0 obj endstream w35R044!i !^\PMk /ProcSet [ /PDF /Text ] <<