Hamilton–Jacobi Theory and the Optical–Mechanical Analogy

foundationsresults+8 moreequations+16 moredepends_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-indices23.1 notationdefinition 23.2: Hamilton's principal function and the Hamilton–Jacobi equation23.2 Hamilton's princ…definition 23.5: Complete integral23.5 Complete integraldefinition 23.13: Additive separability23.13 Additive separab…definition 23.15: Orthogonal Hamiltonian23.15 Orthogonal Hamil…definition 23.16: Stäckel matrix; Stäckel system23.16 Stäckel matrix;…definition 23.28: Action variables23.28 Action variablesdefinition 23.39: Eikonal23.39 Eikonaldefinition 23.52: Lagrangian family; caustic23.52 Lagrangian famil…theorem 23.6: Jacobi23.6 Jacobiproposition 23.7: The principal function is the action23.7 The principal fu…proposition 23.9: Separation of the time23.9 Separation of th…proposition 23.10: The characteristic function is the abbreviated action23.10 The characterist…proposition 23.14: Cyclic coordinates23.14 Cyclic coordinat…theorem 23.17: Stäckel's conditions are sufficient23.17 Stäckel's condit…proposition 23.20: Separability implies integrability23.20 Separability imp…theorem 23.30: Motion in action–angle variables23.30 Motion in action…theorem 23.31: Liouville–Arnold23.31 Liouville–Arnoldtheorem 23.34: Adiabatic invariance of the action23.34 Adiabatic invari…proposition 23.38: Bohr–Sommerfeld and Einstein–Brillouin–Keller quantization23.38 Bohr–Sommerfeld…theorem 23.40: Eikonal and transport equations23.40 Eikonal and tran…proposition 23.41: Rays23.41 Raysequation 23.1: eq:hj-K-zeroeq. (23.1)equation 23.2: eq:hj-equationeq. (23.2)equation 23.5: eq:hj-jacobi-peq. (23.5)equation 23.13: eq:hj-dsdt-chaineq. (23.13)equation 23.14: eq:hj-separate-timeeq. (23.14)equation 23.15: eq:hj-characteristic-equationeq. (23.15)equation 23.23: eq:hj-orthogonal-hamiltonianeq. (23.23)equation 23.25: eq:hj-stackel-conditionseq. (23.25)equation 23.27: eq:hj-stackel-separatedeq. (23.27)equation 23.28: eq:hj-stackel-collapseeq. (23.28)equation 23.38: eq:hj-oscillator-actioneq. (23.38)equation 23.48: eq:hj-magnetic-momenteq. (23.48)equation 23.49: eq:hj-action-variableeq. (23.49)
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