有一个思路，不知对错

In a vertical axis system, the center O is (0,0):

let cat at the bottom (3/2PI), cat run contra-clock-wise

Plan:
1) rat runs all the way vertical to cat's running direction until made a turn of angle of PI/2.
2) Then rat run toward the side along a straight line.

rat speed=v
when both rat and cat made an angle or PI/2, rat (at PI)is (积分(v*cos(0.2t)dt))from center. It's 5v, and in opposite to cat (at 0).

let rat run toward a point (P) at 3rd quarter (let line OP is angle A for horizontal axis). With 余弦定理, we have an equation of v and A.

v=10*(Squre root((PI+A)^2+cosA-1)/((PI+A)^2-1)

I know when A=0, we will have V=10/(PI+1). The minimum can be less, but I didn't know how to find it.

所有跟帖： 

• 好像也是找出最佳路线的问题，楼主快点给答案吧。 -koushi321- ♀ (463 bytes) () 10/22/2008 postreply 14:23:15

• Yes, you made it much more simplified. -passenger101- ♂ (128 bytes) () 10/23/2008 postreply 06:33:25

• update -koushi321- ♀ (592 bytes) () 10/23/2008 postreply 10:08:18

• 回复：猫会反向追，老鼠也可以反向跑 :) -本来清静- ♂ (0 bytes) () 10/23/2008 postreply 15:49:09

• 回复：update -passenger101- ♂ (616 bytes) () 10/23/2008 postreply 16:41:10

• 是我低估了老鼠的智商，对不起。以及v><1的解释 -koushi321- ♀ (1557 bytes) () 10/24/2008 postreply 08:53:39

• 最后一段没有贴全的在这里 -koushi321- ♀ (438 bytes) () 10/24/2008 postreply 09:02:36

• 还不行，再贴一次：最后一段没有贴全的在这里 -koushi321- ♀ (444 bytes) () 10/24/2008 postreply 09:05:37