变质量可控力学系统的广义Mac-Millan方程

Generalized Mac-Millan's Equations for Controllable Variable-Mass Systems

本文利用Gauss 变分原理及加速度空间的广义虚位移关系把广义 Mac-Millan 方程推广到变质量可控力学系统,给出了相应方程的准坐标表述。在此基础上,根据 Nielsen 算子和 Euler 算子的关系得到了变质量可控力学系统的 Nielsen自然方程。最后分别证明了准坐标下变质量可控力学系统广义 Mac-Millan 方程和Appll 方程、Nielsen 自然方程与广义 Nielsen 方程的等价性。

With the Mac--Millan's equations extended to the controllable variable-mass sy-stems by means of Gaussian variational principle and the relationship betweengeneralized virtual displacements in acceleration space, a quasi-coordinateexpression is obtained correspondingly. Nielsen's natural equations are thusgiven for controllable variable--mass systems by virtue of the relation betweenNielsen's operator and Euler's operator. Finally, the equivalence of the general-ized Mac-Millan's equations to Appell's equations and that of Nielsen's naturalequations to generalized Nielsen's are proved,respectively,in system.