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1. The problem statement, all variables and given/known data

There is a circle without mass, radius r. On the edge of the circle there is a mouse, being forced to move around the circle.

The angle the mouse makes with respect to the centre of the circle is called [tex]\theta(t)[/tex]

At the same time, the circle is hold at it's place at a point Q on the edge and is rotated around this point Q with constant angular velocity [tex]\omega[/tex]. Forget about friction.

write down the equation of motion of the mouse.

3. The attempt at a solution

the number of degrees of freedom for this system is 2, [tex]\omega[/tex] and [tex]\theta[/tex]

The Lagrangian L=K-V

[tex]V=0,

K=\frac{m v^2}{2} [/tex]

where [tex] v=v_c+v_\theta[/tex]

and [tex]v_c[/tex] is the velocity of the centre of the circle, and [tex]v_\theta[/tex] is the velocity of the mouse around the circle.

[tex]v_c=\omega l [/tex]

[tex]v_\theta=\theta' l[/tex]

so [tex] \delta J = \delta {\int_{t_1}}^{t_2} \frac{m (\omega l + \theta' l)^2}{2} dt = \delta {\int_{t_1}}^{t_2} \frac{m (\omega^2 l^2 + 2 \omega \theta' l^2 + \theta'^2 l^2)}{2} dt = 0[/tex]

Now I have two problems.

1) is this a good way to write down the Lagrangian?

2) how do I get the [tex] "\delta" [/tex] inside the integral in a good way?

I suppose after that it's integration by parts and setting the integrand equal to zero.

EDIT: I solved the problem myselve today =)

thanks for anyone who was willing to look at it.

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# Lagrange/Hamilton system

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