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Hamiltonian Mechanics
Hamiltonian Mechanics
foundations results +5 more equations +12 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) step_from (declared) step_from (declared) notation 22.1: not:ham-indices 22.1 notation definition 22.2: Hamiltonian 22.2 Hamiltonian definition 22.14: Phase-space coordinate transformation 22.14 Phase-space coor… definition 22.15: Canonical transformation 22.15 Canonical transf… definition 22.26: Lagrange bracket 22.26 Lagrange bracket definition 22.29: Poisson bracket 22.29 Poisson bracket definition 22.40: Symplectic matrix 22.40 Symplectic matrix proposition 22.3: Invertibility of the Legendre map 22.3 Invertibility of… theorem 22.6: Hamilton's equations 22.6 Hamilton's equat… proposition 22.9: Time derivative of the Hamiltonian 22.9 Time derivative… theorem 22.10: Conservation of the Hamiltonian 22.10 Conservation of… proposition 22.11: Hamiltonian and total energy 22.11 Hamiltonian and… proposition 22.17: Transformation conditions 22.17 Transformation c… proposition 22.18: The mixed generating functions 22.18 The mixed genera… lemma 22.20: The symplectic condition 22.20 The symplectic c… theorem 22.22: Poincaré 22.22 Poincaré corollary 22.24: Invariance of the phase-space volume 22.24 Invariance of th… proposition 22.27: Properties of the Lagrange bracket 22.27 Properties of th… proposition 22.30: Properties of the Poisson bracket 22.30 Properties of th… proposition 22.32: Duality of the two brackets 22.32 Duality of the t… equation 22.1: eq:ham-hamiltonian eq. (22.1) equation 22.2: eq:ham-hessian eq. (22.2) equation 22.4: eq:ham-pdot eq. (22.4) equation 22.3: eq:ham-qdot eq. (22.3) equation 22.6: eq:ham-dL eq. (22.6) equation 22.7: eq:ham-dH eq. (22.7) equation 22.10: eq:ham-dhdt eq. (22.10) equation 22.14: eq:ham-ct-P eq. (22.14) equation 22.13: eq:ham-ct-Q eq. (22.13) equation 22.18: eq:ham-generating eq. (22.18) equation 22.21: eq:ham-F2 eq. (22.21) equation 22.33: eq:ham-poincare-integrand eq. (22.33) equation 22.35: eq:ham-lagrange-bracket eq. (22.35) The chain of Hamiltonian Mechanics: 33 of 50 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.