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

• To: mathgroup at smc.vnet.net
• Subject: [mg115553] Help with non-linear system of equations (Trigonometric and Polynomial)
• From: Manjinder Benning <manjbenning at gmail.com>
• Date: Fri, 14 Jan 2011 06:19:20 -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 doesnt 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?

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

```

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