多球平衡问题是中学物理竞赛训练常见题目,理想模型是多个光滑的球,约束在曲面(柱面或半球面)内,或者用绳子悬挂起来,求满足什么样的条件达到平衡.问题关键是求解受力平衡方程,常用方法是几何和三角函数法.其实用代数法(解析几何法)更加直观简单,且容易推广到三维空间.代数法是基于这样的思想:如果一个物理矢量,例如力,已经确定与一个几何矢量方向相同,那么这个物理矢量必定与这个几何矢量成比例关 The problem of multi-ball balance is a common problem in the middle school physics competition training. The ideal model is a number of smooth balls constrained to the surface (cylindrical or hemispherical), or hanging with a rope, to meet the satisfaction of what kind of conditions. Is to solve the force balance equation, the common method is the geometric and trigonometric method.In fact, the use of algebra (analytic geometry) is more intuitive and simple, and easy to generalize to three-dimensional space.Algebra method is based on the idea that if a physical vector, for example Force, has been determined to be the same as a geometric vector, then this physical vector must be proportional to the geometric vector