anonymous
  • anonymous
linearise: dy/dt=a[(1-b)/b]+ba^2+sin(c*a) ; where c is constant.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
i am unsure how to linearise this when only 1 variable is constant. could someone enlighten me how to linearise this with multiple variables?
anonymous
  • anonymous
sorry that should be db/dt
anonymous
  • anonymous
not dy/dt

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freckles
  • freckles
hey what does linearise mean exactly?
freckles
  • freckles
does that mean to solve the differential equation or something else?
anonymous
  • anonymous
clearly, this is a non-linear function, so to make it linear we try to make a general equation of all the tangents where our condition is at steady state.
anonymous
  • anonymous
|dw:1438924011903:dw|
anonymous
  • anonymous
so we try to fit that curve with linear tangents
anonymous
  • anonymous
where the point we know as a basis is the steady state condition.
anonymous
  • anonymous
http://facstaff.cbu.edu/rprice/lectures/lineariz.html
anonymous
  • anonymous
its along these lines..
anonymous
  • anonymous
this is mearly the fundementals for laplace transforms
freckles
  • freckles
@zzr0ck3r do you know how to do this ?
zzr0ck3r
  • zzr0ck3r
Nah, this is some physics/engineering b.s. :) I spent a summer doing it at Uof O but that was 4 years ago and I forgot...
freckles
  • freckles
I was trying to find something easy to follow online but I can't find anything.
anonymous
  • anonymous
haha thanks for helping anyway
anonymous
  • anonymous
we are doing this for process control but i think ive nutted it out
freckles
  • freckles
you think you nutted it out? lol I take that as you did it! :) I would like to see your solution if and when you get time.
anonymous
  • anonymous
to linearise ba^2 we need to partial differentiate each term at steady state
freckles
  • freckles
\[z=ba^2 \\ z_b=a^2 \\ z_a=2ab ?\]
anonymous
  • anonymous
so we get|dw:1438925115302:dw|
anonymous
  • anonymous
so thats a linear approximation of ab^2
anonymous
  • anonymous
so you apply that with all the other non linear terms
freckles
  • freckles
hmm...weird I see where you got the last two terms
freckles
  • freckles
so hey would sin(ca) be \[ \approx \sin( c a_{ss})+c \cos(ca)a'\]
freckles
  • freckles
though that isn't linear :p
anonymous
  • anonymous
yeah i havent figured the sin term yet haha
anonymous
  • anonymous
might have to use an iterative procedure for that...hmm
anonymous
  • anonymous
this is interesting. its only the sin term which is weird to linearise
anonymous
  • anonymous
suggestions?

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