相对均衡解共面性的另一证明  

Another Proof for Relative Equilibrium Solution

作　　者：赵甫荣[1] 唐宗富[1] 

机构地区：[1]绵阳师范学院数学与计算机科学学院,四川绵阳621000

出　　处：《绵阳师范学院学报》2009年第8期12-13,21,共3页Journal of Mianyang Teachers＇ College

摘　　要：牛顿n-问题是主要研究在牛顿运动定律和万有引力的作用下,天体的运动规律。一般而言,n-体问题就是一个常微分方程组。由于方程组是非线性的,当天体的个数大于3时,n-体问题不可能完全解决,故转而求特解,相对均衡解就是其中之一。该文利用微分几何对相对均衡解共面性给出另一证明。证明过程揭示了相对均衡解的几何性质。The ＂Newtonian N- bodies move in settings where the dynamics are dictated by Newton＇s law of motion and the law of gravity. In general, n - body problem is a system of ordinary differential equations being nonlinear. There is good evidence that the general n -body problem is not solvable when there exist more than three spherical bodies. It is necessary to look for special solutions one of which is relative equilibrium solution. In this article, another proof for relative equilibrium solution is given by using differential geometry. The process shows the geometric features of relative equilibrium solution.

关 键 词：N体问题 相对均衡解 中心构型 共面 扰率 

分 类 号：O175.1[理学—数学]