Treatise of Physics

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proposition 22.41 Symplectic form of Hamilton's equations

open in the book · parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1360 · p. 820

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proposition 22.41: Symplectic form of Hamilton's equations22.41equation 22.4: eq:ham-pdot22.4equation 22.3: eq:ham-qdot22.3equation 22.56: eq:ham-symplectic-matrix22.56remark 22.42: What the matrix form is for22.42proof : ch:05-hamiltonian-mechanics@proof-18proofdefinition 32.54: The kicked rotor and the standard map32.54definition 24.14: Hamiltonian vector field24.14proposition 22.9: Time derivative of the Hamiltonian22.9theorem 22.34: Evolution of a phase-space function22.34theorem 24.23: Poincaré–Cartan integral invariant24.23proposition 24.3: Even dimension and the canonical basis24.3remark 24.27: Fixing a scale, so that a ``ball'' means something24.27theorem 25.3: The bracket is a Lie bracket25.3remark 22.5: Units22.5

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depends_on → eq:ham-pdot declared parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1367
depends_on → eq:ham-qdot declared parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1367
depends_on → eq:ham-symplectic-matrix declared parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1367
depends_on ← What the matrix form is for declared parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1407
proves ← ch:05-hamiltonian-mechanics@proof-18 declared parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1370