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Homework Statement
Homework Equations
$$\mathcal{L}=TU$$
$$\omega= \frac{d\phi}{dt}$$
$$I=mr^{2}$$
The Attempt at a Solution
My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following:
$$K.E t=\frac{1}{2}m(\dot{x}^{2}+\dot{y}^{2}+\dot{z}^{2})=\frac{1}{2}m(1+(\frac{R}{\lambda})^{2}) \dot{z}^{2}$$
But as far as I understood, there is rotational kinetic energy as well, namely the following
$$K.E r= \frac{1}{2}I \omega^{2} = \frac{1}{2}mR^{2} \frac{\dot{z}^2}{\lambda^2}$$
The helix is just the trajectory of the particle. If you look at the helix from above you see a circle. Furthermore, the angle depend on ##z##, which I believe support my idea.
I usually prefer looking at the solutions. Especially when I self study. I looked at two different sources from two different universities, none include rotational kinetic energy! Am I wrong?
Source 1
Source 2
Footnote: Classical Mechanics, By Taylor. Problem 7.20
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