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Hamilton–Jacobi Theory and the Optical–Mechanical Analogy
Hamilton–Jacobi Theory and the Optical–Mechanical Analogy
foundations results +8 more equations +16 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) step_from (declared) step_from (declared) step_from (declared) step_from (declared) notation 23.1: not:hj-indices 23.1 notation definition 23.2: Hamilton's principal function and the Hamilton–Jacobi
equation 23.2 Hamilton's princ… definition 23.5: Complete integral 23.5 Complete integral definition 23.13: Additive separability 23.13 Additive separab… definition 23.15: Orthogonal Hamiltonian 23.15 Orthogonal Hamil… definition 23.16: Stäckel matrix; Stäckel system 23.16 Stäckel matrix;… definition 23.28: Action variables 23.28 Action variables definition 23.39: Eikonal 23.39 Eikonal definition 23.52: Lagrangian family; caustic 23.52 Lagrangian famil… theorem 23.6: Jacobi 23.6 Jacobi proposition 23.7: The principal function is the action 23.7 The principal fu… proposition 23.9: Separation of the time 23.9 Separation of th… proposition 23.10: The characteristic function is the abbreviated action 23.10 The characterist… proposition 23.14: Cyclic coordinates 23.14 Cyclic coordinat… theorem 23.17: Stäckel's conditions are sufficient 23.17 Stäckel's condit… proposition 23.20: Separability implies integrability 23.20 Separability imp… theorem 23.30: Motion in action–angle variables 23.30 Motion in action… theorem 23.31: Liouville–Arnold 23.31 Liouville–Arnold theorem 23.34: Adiabatic invariance of the action 23.34 Adiabatic invari… proposition 23.38: Bohr–Sommerfeld and Einstein–Brillouin–Keller
quantization 23.38 Bohr–Sommerfeld… theorem 23.40: Eikonal and transport equations 23.40 Eikonal and tran… proposition 23.41: Rays 23.41 Rays equation 23.1: eq:hj-K-zero eq. (23.1) equation 23.2: eq:hj-equation eq. (23.2) equation 23.5: eq:hj-jacobi-p eq. (23.5) equation 23.13: eq:hj-dsdt-chain eq. (23.13) equation 23.14: eq:hj-separate-time eq. (23.14) equation 23.15: eq:hj-characteristic-equation eq. (23.15) equation 23.23: eq:hj-orthogonal-hamiltonian eq. (23.23) equation 23.25: eq:hj-stackel-conditions eq. (23.25) equation 23.27: eq:hj-stackel-separated eq. (23.27) equation 23.28: eq:hj-stackel-collapse eq. (23.28) equation 23.38: eq:hj-oscillator-action eq. (23.38) equation 23.48: eq:hj-magnetic-moment eq. (23.48) equation 23.49: eq:hj-action-variable eq. (23.49)
The chain of Hamilton–Jacobi Theory and the Optical–Mechanical Analogy: 35 of 59 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.
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