高阶非完整系统相对论性的Gibbs-Appell型方程

Relativistic Gibbs-Appell′s Equations of High-order Nonholonomic Mechanical System

国内外对非完整系统的 Gibbs-Appell 型方程(简称 G-A 方程)的研究正在逐步深入.本文从相对论性的万有 D'Alembert 原理出发,构造了一些必要的函数,应用 Appell 变换,并根据狭义相对论及变质量等力学条件,将 G-A 方程推广到高阶非完整相对论性的力学系统中,建立了广义坐标和准坐标下相对论的高阶非完整的 G-A 方程和积分变分原理,使方程具有更为广泛的适用性.可在核能控制。

The importance of various nonholonomic restraints to modern engineering technique has appeared gradually in recent years.The Gibbs-Appell's equations for nonholonomic sys- tems are being deeply studied by home and abroad scholars.Compared with the original equations,these new results are not only more concise in form,but also widcr in application. In this paper,applying the theory of Appell transform,forming some necessary func- tions,and considering the mechanical conditions of special relativity and variable mass,the relativistic Gibbs-Appell's equations and integral variational principle are derived from the relativistic universal D'Alembert's perinciple.They are expressed by generalized coordinates and quasi-coordinates and can be used in high-order nonholonomic mechanical system.Ob- viously,they will be applied to the fields of nuclear energy control,particle physics and space technology.