(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Lagrange/Hamilton system

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Lagrange/Hamilton system

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**