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anonymous

  • one year ago

linearise: dy/dt=a[(1-b)/b]+ba^2+sin(c*a) ; where c is constant.

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  1. anonymous
    • one year ago
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    i am unsure how to linearise this when only 1 variable is constant. could someone enlighten me how to linearise this with multiple variables?

  2. anonymous
    • one year ago
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    sorry that should be db/dt

  3. anonymous
    • one year ago
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    not dy/dt

  4. freckles
    • one year ago
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    hey what does linearise mean exactly?

  5. freckles
    • one year ago
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    does that mean to solve the differential equation or something else?

  6. anonymous
    • one year ago
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    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.

  7. anonymous
    • one year ago
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    |dw:1438924011903:dw|

  8. anonymous
    • one year ago
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    so we try to fit that curve with linear tangents

  9. anonymous
    • one year ago
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    where the point we know as a basis is the steady state condition.

  10. anonymous
    • one year ago
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    http://facstaff.cbu.edu/rprice/lectures/lineariz.html

  11. anonymous
    • one year ago
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    its along these lines..

  12. anonymous
    • one year ago
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    this is mearly the fundementals for laplace transforms

  13. freckles
    • one year ago
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    @zzr0ck3r do you know how to do this ?

  14. zzr0ck3r
    • one year ago
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    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...

  15. freckles
    • one year ago
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    I was trying to find something easy to follow online but I can't find anything.

  16. anonymous
    • one year ago
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    haha thanks for helping anyway

  17. anonymous
    • one year ago
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    we are doing this for process control but i think ive nutted it out

  18. freckles
    • one year ago
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    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.

  19. anonymous
    • one year ago
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    to linearise ba^2 we need to partial differentiate each term at steady state

  20. freckles
    • one year ago
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    \[z=ba^2 \\ z_b=a^2 \\ z_a=2ab ?\]

  21. anonymous
    • one year ago
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    so we get|dw:1438925115302:dw|

  22. anonymous
    • one year ago
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    so thats a linear approximation of ab^2

  23. anonymous
    • one year ago
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    so you apply that with all the other non linear terms

  24. freckles
    • one year ago
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    hmm...weird I see where you got the last two terms

  25. freckles
    • one year ago
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    so hey would sin(ca) be \[ \approx \sin( c a_{ss})+c \cos(ca)a'\]

  26. freckles
    • one year ago
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    though that isn't linear :p

  27. anonymous
    • one year ago
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    yeah i havent figured the sin term yet haha

  28. anonymous
    • one year ago
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    might have to use an iterative procedure for that...hmm

  29. anonymous
    • one year ago
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    this is interesting. its only the sin term which is weird to linearise

  30. anonymous
    • one year ago
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    suggestions?

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