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Solving a system of nonlinear differential equations

  1. Mar 23, 2010 #1
    1. The problem statement, all variables and given/known data
    I'm working on a problem for my robotics class and could really use some help. I am suppose to be modeling a planar scara manipulator and have managed to come up with two nonlinear differential equations that describe the system; they are shown below. [tex]\Theta_{1}[/tex] and [tex]\Theta_{1}[/tex] are time dependent.

    How would I solve these two equations in matlab for [tex]\Theta_{1},\dot{\Theta_{1}}, \Theta_{2},[/tex] and [tex] \dot{\Theta_{2}} [/tex] if i am given the initial conditions of [tex]\Theta_{1},\dot{\Theta_{1}}, \Theta_{2},[/tex] and [tex]\dot{\Theta_{2}} [/tex]. As well as [tex]\tau_{1}[/tex] and [tex]\tau_{2}[/tex]? I am suppose to plot [tex]\Theta_{1}[/tex] and [tex]\Theta_{2}[/tex] for a time period of 30 seconds.

    Any help would be appreciated


    2. Relevant equations
    [tex]\tau_{1}= (3+cos\Theta_{2})\ddot{\Theta_{1}}+\ddot{\Theta_{2}}+\dot{\Theta_{1}^{2}}sin\Theta_{2}-(\dot{\Theta_{1}}+\dot{\Theta_{2}})^{2}sin\Theta_{2}+9.8cos(\Theta_{1}+\Theta_{2})+(\ddot{\Theta_{1}}+\ddot{\Theta_{2}})cos\Theta_{2}+19.6cos\Theta_{1}[/tex]
    [tex]\tau_{2}= \ddot{\Theta_{1}}+\ddot{\Theta_{2}}+\ddot{\Theta_{1}}cos\Theta_{2}+\dot{\Theta_{1}^{2}}sin\Theta_{2}+9.8cos(\Theta_{1}+\Theta_{2})[/tex]
    Last edited: Mar 23, 2010
  2. jcsd
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