Asymptotic motions and the problem of the inversion of the Lagrange-Dirichlet theory
摘要：
The motion of natural mechanical systems tending to equilibrium with infinitely increasing time is investigated with particular reference to degenerate cases where several frequencies of small oscillations are reduced to zero. A proof is presented for a theorem on the existence of asymptotic trajectories assuming that Maclaurin's series of potential energy has the form V2 + Vm + V(m+1) + ... (where Vs is a homogeneous form of the exponent s) and that the function V2 + Vm does not have a local minimum in the equilibrium position. This theorem is then used to solve the problem of the existence of asymptotic trajectories in the case of simple and unimodal singularities of potential energy for which canonic normal forms are known.
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关键词：
alcohols (benzene compounds reactions of organo-metal compounds C-C bond formation organocatalysis
DOI：
10.1016/j.tetlet.2014.10.101
年份：
2014
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