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单词 HamiltonianVectorField
释义

Hamiltonian vector field


Let (M,ω) be a symplectic manifoldMathworldPlanetmath, and ω~:TMT*M be the isomorphism from the tangentbundleMathworldPlanetmath to the cotangent bundleMathworldPlanetmath

Xω(,X)

and let f:M is a smooth function.Then Hf=ω~-1(df)is the Hamiltonian vector field of f. The vector field Hf is symplectic (http://planetmath.org/SymplecticVectorField),and a symplectic vector field X is http://planetmath.org/node/6410Hamiltonian if and only if the 1-form ω~(X)=ω(,X) is exact.

If T*Q is the cotangent bundle of a manifoldMathworldPlanetmath Q, which is naturally identified with the phasespace of one particle on Q, and f is the Hamiltonian, then the flow of the Hamiltonianvector field Hf is the time flow of the physical system.

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更新时间:2025/5/4 17:34:42