Help with non-linear system of equations (Trigonometric and Polynomial)

*To*: mathgroup at smc.vnet.net*Subject*: [mg115578] Help with non-linear system of equations (Trigonometric and Polynomial)*From*: Manjinder Benning <manjbenning at gmail.com>*Date*: Sat, 15 Jan 2011 04:45:29 -0500 (EST)

Hi i am trying to do some 3D modeling by finding a 6 unknown 6 equation simultaneous system. I am using the equation: Cos(a) = A.B/|A||B| where A and B are lines (vectors) in 3 space. a is the angle between the lines. When i run the calculation, Mathematica just runs forever and doesn't come to a solution. It would be great if a closed form solution could be found. I am understanding that it is difficult to solve systems with polynomial and trig parts? Description of Problem: So i have 3 points in 3-space. Pl (Xl, Yl, Zl) - A constant point in the air Pc(Xc, Yc, Zc) - A constant point on the ground (Z=0) Pe's (Xe_n, Ye_n, Ze_n) - A series of points that lay on the edges of an ellipse co-planar to Z=0 (which are known experimentally) A - The angle between the line (Pl -> Pc) and each (Pl -> Pe_n) Due to the geometry of the problem (a ellipse) angle A is constant. Are there any methods i can use to make it easier to solve (ie bounding the problem) or am i dreaming that i will find a closed form solution? ...any help would be appreciated: Heres the code: eq1 =Cos[A] == ((Xc - Xl)*(Xe1-Xl) + (Yc-Yl)*(Ye1-Yl) + (-Zl)*(-Zl))/Sqrt[( (Xc - Xl)^2 + (Yc-Yl)^2+(-Zl)^2 ) * ((Xe1-Xl)^2 +(Ye1-Yl)^2+(-Zl)^2)] eq2 =Cos[A] == ((Xc - Xl)*(Xe2-Xl) + (Yc-Yl)*(Ye2-Yl) + (-Zl)*(-Zl))/Sqrt[( (Xc - Xl)^2 + (Yc-Yl)^2+(-Zl)^2 ) * ((Xe2-Xl)^2 +(Ye2-Yl)^2+(-Zl)^2)] eq3 =Cos[A] == ((Xc - Xl)*(Xe3-Xl) + (Yc-Yl)*(Ye3-Yl) + (-Zl)*(-Zl))/Sqrt[( (Xc - Xl)^2 + (Yc-Yl)^2+(-Zl)^2 ) * ((Xe3-Xl)^2 +(Ye3-Yl)^2+(-Zl)^2)] eq4 =Cos[A] == ((Xc - Xl)*(Xe4-Xl) + (Yc-Yl)*(Ye4-Yl) + (-Zl)*(-Zl))/Sqrt[( (Xc - Xl)^2 + (Yc-Yl)^2+(-Zl)^2 ) * ((Xe4-Xl)^2 +(Ye4-Yl)^2+(-Zl)^2)] eq5 =Cos[A] == ((Xc - Xl)*(Xe5-Xl) + (Yc-Yl)*(Ye5-Yl) + (-Zl)*(-Zl))/Sqrt[( (Xc - Xl)^2 + (Yc-Yl)^2+(-Zl)^2 ) * ((Xe5-Xl)^2 +(Ye5-Yl)^2+(-Zl)^2)] eq6 =Cos[A] == ((Xc - Xl)*(Xe6-Xl) + (Yc-Yl)*(Ye6-Yl) + (-Zl)*(-Zl))/Sqrt[( (Xc - Xl)^2 + (Yc-Yl)^2+(-Zl)^2 ) * ((Xe6-Xl)^2 +(Ye6-Yl)^2+(-Zl)^2)] Solve[{eq1,eq2,eq3,eq4,eq5, eq6},{A,Xl,Yl,Zl,Xc,Yc}] much gratitude to all things Mathematica! Manjinder. -- www.thepowerofyang.com