Lagrangian function of pendulum

  • Thread starter Grand
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  • #1
Grand
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Homework Statement


Find the Lagrangian and the Lagrangian equations for this pendulum (see the picture). Radius of circle is a, mass of the bob is m and l is the length of the pendulum when it hangs straight down.


Homework Equations





The Attempt at a Solution


I obtain:
[tex]L=\frac{1}{2}m(a^2\dot{\theta}^2+(l+a\theta)^2\dot{\theta}^2)-mg(a\sin\theta-(l+a\theta)\cos\theta)[/tex]
while the answer in the book misses the term [tex]a^2\dot{\theta}^2[/tex] - where have I gone wrong?
Thank you in advance.
 

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Answers and Replies

  • #2
ehild
Homework Helper
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How did you get that extra term? The x,y coordinates of the bob with respect to the centre of the circle are x=a cos(θ)+(l+a)sin(θ), y=sin(θ)-(l+a)cos(θ). Take the time derivatives to get the x, y components of velocity.

ehild
 

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