Solve Equation numerically for variable
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Need to solve this problem for w:
0 = A + Bcos(w) + Ccos(w) ( A,B,C Constants)
Bounds should be 0-180 for this problem I believe, two solutions possible?
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Star Strider
le 21 Juil 2016
If ‘A’, ‘B’ and ‘C’ are matrices, then:
w = acos(-(B+C)\A);
assuming that the matrices have the appropriate dimensions, and the resulting argument matrix ‘(-(B+C)\A)’ elements are all between -1 and +1.
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Star Strider
le 21 Juil 2016
The Symbolic Math Toolbox comes up with these solutions for ‘w’ that would also work for matrices:
syms A B C w
w_sol = solve(A == B*cos(w) + C*sin(w), w);
w_sol = simplify(w_sol, 'steps',10)
-log((A + (A^2 - B^2 - C^2)^(1/2))/(B - C*1i))*1i
-log((A - (A^2 - B^2 - C^2)^(1/2))/(B - C*1i))*1i
Use the sqrtm and logm functions. Also see the funm function. If you know that your matrices will always be real or positive, you can tell the Symbolic Math Toolbox to assume that. It may simplify the result.
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