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Topic: Using Solve/FSolve for Multiple Trig Equations
Replies: 7   Last Post: May 4, 2013 8:44 AM

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 Bruno Luong Posts: 9,822 Registered: 7/26/08
Re: Using Solve/FSolve for Multiple Trig Equations
Posted: May 1, 2013 3:16 PM

"Jung" wrote in message <klrf49\$bq1\$1@newscl01ah.mathworks.com>...
> Hello,
>
> I am trying to solve for:
> y
> r
> p
>
> in the following equations where I, J, K are known.
>
> I = siny * sinr + cosy * sinp * cosr
> J = -siny * cosr + cosy * sinp * sinr
> K = cosy * cosp
>

Your system looks like solving for three Euler angles knowing one column of the rotation matrix. See formulas before "Quaternion".

http://en.wikipedia.org/wiki/Euler_angles

(-J,I,K)' is the last column of [Z1*X2*Y3], where
theta1 = r;
theta2 = -p;
theta3 = y.

In this case meaning that you want to find the solid rotation, from knowing how end up only one unit vector after rotation.

I'm sorry to tell that you don't have unique solution [I wrote this affirmation somewhere in this newsgroup]. Thus your system is not solvable.

Bruno

Date Subject Author
5/1/13 Jung
5/1/13 Nasser Abbasi
5/1/13 Alan Weiss
5/1/13 Bruno Luong
5/2/13 Bruno Luong
5/2/13 Bruno Luong
5/4/13 Bruno Luong
5/1/13 Bruno Luong