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Asimov pendulum

  1. Apr 19, 2014 #1
    I am reading about the Asimov pendulum (see figure)

    The aceleration in spherical coordinates is

    ##\vec{a} =( R \dot{\theta}^2 - R \omega^2 \sin ^2 \theta) \hat{r} + (R \ddot{\theta} - R \omega ^2 \sin \theta \cos \theta ) \hat{\theta} + (2R \dot{\theta} \omega \cos \theta) \hat{\phi}##

    The forze is:

    ##-mg\hat{y}= -mg\cos(\frac{\pi}{2}-\theta) \hat{\theta} =-mg\sin(\theta) \hat{\theta}##

    If i analize the theta component i find the answer for the equation of motion

    ##R \ddot{\theta} - R \omega ^2 \sin \theta \cos \theta = -g\sin(\theta)##

    But, what happen with the other component of equation of motion?, why this does not appear in the books?

    ##R \dot{\theta}^2 - R \omega^2 \sin ^2 \theta =0##
    ##2R \dot{\theta} \omega \cos \theta=0##
    In the last equation neither of the terms are zero.

    Pd: I does not want to use the Lagran
     

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  3. Apr 20, 2014 #2

    Simon Bridge

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    Try solving the equation and find out.
     
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