论文部分内容阅读
若物理矢量是变化的,且其矢端始终落在一个圆周上,作出这个圆,便是“矢量圆”.用矢量圆分析动态问题非常方便. 例1 某人划船,在静水中速度为v1=3m/s,若他在水速为v2=5m/s的河中行驶,要使船渡河的路径最短,则他应怎样控制船的航向? 分析 若v合垂直河岸,则必有v1>v2,这与题给数据矛盾.进一步分析可知:v合只能与v2成一角度θ,且指向下游,若θ越大,则s越短.如图1所示,v1、v2、v合构成一个矢量三角形,其中,v1的变化应在一矢量圆上.易知,v合与矢量圆相切时,s最短.
If the physical vector is changing, and its vector end always falls on a circle, making this circle is a “vector circle”. It is very convenient to analyze dynamic problems with vector circles. Example 1 Someone rowing, speed in still water For v1=3m/s, if he is driving in a river with a water speed of v2=5m/s, what should he do to control the ship’s course if he wants to make the shortest way to cross the river? If there is a vertical river bank, there must be v1. > v2, this is contradictory to the question data. Further analysis shows that: v can only be an angle θ with v2, and points downstream, if θ is larger, s is shorter. As shown in Figure 1, v1, v2, v Constructs a vector triangle, in which the variation of v1 should be on a vector circle. It is easy to know that s is the shortest when v is tangent to the vector circle.