ranyai12
Consider the spring model
x''−3x+3(x^3)=0
where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in x and y=x.
x' =
y' =
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TuringTest
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I am thinking that there is a typo...
are you sure it says rewrite as \[y=x\]?
mahmit2012
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y=x'
mahmit2012
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and we should find out (x,y)=(x,x')=state space vector.
ranyai12
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idk thatswhat tge directions say exactly i just copied and pasted we also had to solve for critical points which i already did
mahmit2012
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|dw:1344182958485:dw|
ranyai12
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whats whats y= to?
mahmit2012
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|dw:1344183055225:dw|
ranyai12
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wait howd you solve that?
ranyai12
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yea i got the critical points but I used the jacobie eigenvalue
ranyai12
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i mean jacoby value
mahmit2012
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the problem has three critical points that I showed you.
ranyai12
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how did ou see that x'=y
mahmit2012
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Those of the problems like yours we should define a state space vector that includes independent component ,usually x and its derivatives are selected as components.
ranyai12
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whats space vector?
mahmit2012
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state space vector is a vector which include all independent variable in a system.
for example place velocity . acceleration are three component require to know in a third order system.
mahmit2012
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So (x,v,a)=(x,x',x") is a state space vector.
ranyai12
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oh ok! thank you!!
mahmit2012
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you're welcome.