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Try to solve this system of equations

Posted 9 years ago
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Hello everyone I try to solve this system shown below.

Solve[r2 == 
   r1 Cos[\[Theta]\[Alpha]1 + \[CapitalDelta]\[Theta] - \[Theta]\
\[Alpha]2] + (h + vh \[Tau]1) Cos[\[Theta]\[Alpha]2] + (k + 
       vk \[Tau]1) Sin[\[Theta]\[Alpha]2] &&
  spo2 == -spo1 Cos[\[Theta]\[Alpha]1 + \[CapitalDelta]\[Theta] - \
\[Theta]\[Alpha]2] + vh Sin[\[Theta]\[Alpha]2] - 
    vk Cos[\[Theta]\[Alpha]2] &&
  \[Tau]1 spo1 == \[CapitalDelta]\[Theta] r1 + l &&
  \[CapitalDelta]\[Theta] == \[Beta] - \[Psi] - Pi/2 &&
  \[Psi] == ArcCos[(spo2^2 - so1o2^2 - spo1 ^2)/(2 spo1 so1o2)],
 {\[CapitalDelta]\[Theta], \[Theta]\[Alpha]2, \[Tau]1, spo1, \[Psi]}]

There are 5 unknown variables and 5 equations. This system is quite complex because of trigonometric functions. I do not know how to solve them. It took a long time and I haven't got the answer yet. It's still running.

Anyone can help me? Thank you very very very much in advance.


Nonlinear equations are tough. You can't guarantee they have a solution and there's no single trick or method for finding the solution. If Mathematica doesn't find a solution, then its pretty likely that a symbolic solution doesn't exist. I wasn't able to find a simple way to improve the equations. You can either:

  • Simplify the equations somehow,usually by linearizing something like a Cosine or Sine.
  • Try using a numerical method to search for a solution. NSolve or FindRoot can be used here.
POSTED BY: Sean Clarke
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