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A homogeneous cylinder of mass M and radius R can roll without

slipping on a horisontal table. One end of the cylinder reaches a tiny

bit out over the edge of the table. At a point of the pheriphery of the

end surface of the cylinder, a homogeneous rod is attached to the

cylinder by a frictionless joint. The rod has mass m and length l. Find

Lagrange's equations for the generalised coordinates phi (angle in the cylinder) and theta (rod's angle)

according to the figure, and determine the frequences of the principal

modes of small oscillations. (Principal frequences = roots of

characteristic equation.)

___________________________

I have a attached a figure.

With

[tex]T = 1/4MR^2 \dot{\phi}^2 + 1/6ml^2 \dot{\theta}^2[/tex]

[tex]U=mg[R(1-cos\phi)+l/2(1-cos\theta)][/tex]

[tex]L=T-U[/tex]

I get the equation of motions

[tex]\ddot{\phi}=\frac{2mg}{MR}\phi[/tex]

[tex]\ddot{\theta}=\frac{3g}{2l}\theta[/tex]

which is the correct answer except a factor 1/3 in the equation for phi.

But it feels like i have done some big misstakes computing T.

I havent included that the rod is attached to the cylinder. And im not sure how to do this.

And i havent included the the cylinder is rolling ?!?

Any ideas?

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# Homework Help: Mechanics - rod attached to cylinder

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