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I need to model human hairs in Matlab by solving ODEs, but I'm struggling to understand what to do. Here is all of the provided information:

enter image description here

I've been asked to write a function returning the $(x,y,z)$ coordinates of the hairs given $L$, $R$, $f_x$ and a list of values for $\theta(L)$ and $\phi(L)$. I'm just not sure what sure what this $(x,y,z)$ coordinate is for because I can't see how one coordinate can help me - is it a set of coordinates which would plot each hair?

I feel like I'm missing something here and would really appreciate a few pointers because I just don't know where to start. Thanks in advance.

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  • $\begingroup$ $x,y,z$ are functions of $s$. So you are not getting a single point, but an entire curve - the curve that the hair follows. $\endgroup$ Commented Dec 6, 2015 at 22:27
  • $\begingroup$ Thank you for your reply, that makes perfect sense. I've been able to make a lot of progress with this and couldn't have done it without your input. $\endgroup$
    – tom982
    Commented Dec 7, 2015 at 2:41

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You have differential equation $(4)$ with a boundary conditions $(5)$. One of them is a parameter $\theta (L)$ you get as an input. Actually you get a list of them, so each one is per different hair.

type doc ode45 in matlab to get help on a function that can solve such equation(read the documentation there is a list of such functions).

Once you solved $(5)$ you use the solutions to solve 3 differential equations $(6)$ with the initial conditions given by the formulas $(1),(2),(3)$. Note that you have to solve $(6)$ one per given $\theta (L)$. The solutions of equations $(6)$ are $(x,y,z)$ is what you looking for.

Note, $\phi$ is a constant as it stated after equation $(3)$, so $\phi(s)=\phi(L)$.

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  • $\begingroup$ Thank you so much for taking the time to reply, I really appreciate it. You've explained it so clearly and I've almost finished the assignment now. Thanks again. $\endgroup$
    – tom982
    Commented Dec 7, 2015 at 2:42

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