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A particle of mass m is constrained to move on the inside surface of a
smooth cone of half-angle a (i.e., z =r cot a) as shown in the figure to a
gravitational force. The particle is subject to a gravitational force (i.e.,
g=-gk ).
(a) Determine the Lagrangian for this particle in terms of the generalized
coordinates r and 0.
(b) Determine Lagrange's equations of motion for this particle.

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