推 stma:感謝解答! 原版已找不到 但是知道這種題目解法就好了! 05/05 02:23
y※ 引述《stma (BBS)》之銘言：
: 題目大致如下
: dX1/dt = 6X1 - 6X2
: dX2/dt = 4X1 - 5X2
: 其中X1 X2皆為時間t之函數
: Find two variables Y1 Y2 which can de-couple the dynamic motion
: of the system
: Express Y1 Y2 as linear combination of X1 X2
: 題目要把X代換成Y 然後每一方程式只含有其中一樣函式 是這樣嗎?
: 請問要如何下手呢?
. [6 -6]
X = AX ,A =[4 -5]
AU = λU , (A-λI)U = 0 ,λ = -2,3
當λ = -2
[8 -6] [3]
[4 -3]U = 0 ,U = C1[4]
當λ = 3
[3 -6] [2]
[4 -8]U = 0 ,U = C2[1]
[3 2] [-2 0] -1
取S = [4 1] ,D = [ 0 3] ,A = SDS
令 X = SY 代入
. . -1 .
SY = ASY ,SY = SDS SY ,Y = DY
[3 2]
X = [4 1]Y ---->題目要的??
. [-2 0]
Y = [ 0 3]Y
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 118.167.136.210