关于角量的标量性与矢量性

The Character of Scalar Quantity and Vector Quantity About Angular Quantity

无限小角位移、有限大角位移、角速度、平均角速度、角加速度、平均角加速度和角坐标的增量以及角坐标对时间的一阶和二阶导数不仅是物理学中常用的物理量 ,而且也是很重要的物理概念。物理量又分为标量、矢量和张量 ,若物理量是矢量 ,它应服从矢量的加法法则 ,即两个矢量相加时 ,相加次序不影响它的结果 ,由A→ +B→ =B→+A→ 所得到的最终结果相同。根据这一原则 ,首先 ,将质点对两个坐标轴角坐标的变化等效的转化成坐标系对坐标轴的转动 ;其次 ,交换坐标系对坐标轴的转动次序 ,由此得到的同一矢量两个不同的结果表达式。结果表明 ,无限小的角位移、角速度、平均角加速度、角加速度都是矢量 ,而有限大的转角 。

Infinitely small angular displacement finitely great angular displacement angular velocity mean angular velocity angular acceleration mean angular acceleration and the increment of angular coordinate as well as the first and second derivative of angular with respect to time is not only the physical quantities which often being used but also important physical quantities. The physical quantities is divided up scalar quantity vector quantity and tensor. If physical quantity is vector quantity it must obey the addition rule of vector quantity, that is to say, when two vector quantities is added, its result is not influenced by adding order. In other words, the result is same as the result of A-> + B-> = B-> + A->. According to this rule, first of all, the change of angular coordinate of particle with respect to two coordinate axis transforms equivalently the turn of coordinate system with respect to coordinate axis. In the second place, the turn order of coordinate system with respect with coordinate axis is exchanged. The two different result express formula of the same vector is obtained, the result show that infinitely small angular displacement angular velocity mean angular acceleration angular acceleration are all vector quantity finitely great angular displacement the increment of angular coordinate of particle in coordinate system and the derivative of angular coordinate with respect to time as well are all scalar quantity.