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Simple dynamics equation

  1. Feb 8, 2013 #1
    pendulum2.png

    InvertedPendulum_SystemModeling_eq17002.png

    Didn't get this equation which is written for the pendulum part of the cart.
    Must be easy but couldn't get it.
     
  2. jcsd
  3. Feb 8, 2013 #2

    AlephZero

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    It is just "force = mass x acceleration" in the x direction, for the center of mass of the rod. (The length of rod isn't shown on your diagram, but if the equation is correct it is 2l, not l).

    The ##\ddot\theta## term is from the tangential acceleration of the rod.

    The ##\dot\theta^2## term is the from the radial (centripetal) accleration.
     
  4. Feb 8, 2013 #3
    It's a little clearer now, but didn't understand the centripetal force component.

    Isn't it

    df86712e000fe347516b8f39b9490815.png
     
  5. Feb 8, 2013 #4

    AlephZero

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    Yes.

    You also know ##v = \omega r## and ##\omega = \dot\theta##

    The centripetal force is radial (along the length of the rod), but the equation is for the component of the force in the X direction.
     
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