A generalization of the Helmholtz conditions for the existence of a first‐order Lagrangian
A generalization of the Helmholtz conditions for the existence of a first‐order Lagrangian
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DOI：
10.1002/zamm.200510278
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发表时间：
2006-09
期刊：
影响因子：
--
通讯作者：
G. Kielau;P. Maisser
中科院分区：
文献类型：
--
作者：
G. Kielau;P. Maisser
本文讨论了Helmholtz条件的推广，该条件与给定的一组二阶常微分方程相关的一阶动力势的存在性。这种扩展影响了对由于耗散而不是自伴的常微分方程系统的考虑。给出了同时存在两个状态函数--拉格朗日函数和耗散函数--的充分必要条件，这两个状态函数都是一阶的，使得给定的二阶常微分方程组由著名的拉格朗日方法得到。
The paper deals with a generalization of Helmholtz' conditions for the existence of a first‐order kinetic potential related to a given set of 2nd order ordinary differential equations. The extension affects the consideration of such ODE systems which are not self‐adjoint due to dissipation. Necessary and sufficient conditions are given for the simultaneous existence of two state functions – a Lagrangian and a dissipation function – both of the first‐order such that the given set of 2nd order ODE results from the well‐known Lagrangean approach.