Find its lagrangian in terms of the euler angles

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Reference no: EM131383698

Spinning hoop on a smooth floor A uniform circular hoop of radius a rolls and slides on a perfectly smooth horizontal floor. Find its Lagrangian in terms of the Euler angles, and determine which of the generalised momenta are conserved. [Suppose that G has no horizontal motion.]

Investigate the existence of motions in which the angle between the hoop and the floor is a constant α. Show that Ω, the rate of steady precession, must satisfy the equation

cos αΩ² - 2nΩ - 2(g/a)cot α = 0,

where n is the constant axial spin. Deduce that, for n ≠ 0, there are two possible rates of precession, a faster one going the ‘same way' as n, and a slower one in the opposite direction.

[These are interesting motions but one would need a very smooth floor to observe them.]

Reference no: EM131383698

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