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单词 Hamiltonian mechanics
释义
Hamiltonian mechanics

Mathematics
  • A rewriting of Lagrange’s equations which foreshadowed advances in statistical mechanics and quantum theory. In the notation of Lagrange’s equations, we set pi=L/q˙i and introduce the Hamiltonian

    H(q,p,t)=i=1npiqiL(q,p,t).

    Hamilton’s equations then have the form

    dqidt=Hpi,dpidt=Hqi.


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