A particle of mass (m) slides inside a smooth hemispherical bowl of radius (R). Use spherical coordinates
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A particle of mass \(m\) slides inside a smooth hemispherical bowl of radius \(R\). Use spherical coordinates \(r, \theta\) and \(\phi\) to describe the dynamics.
(a) Write the Lagrangian in terms of generalized coordinates and solve the dynamics.
(b) Repeat the exercise using a Lagrange multiplier. What does the multiplier measure in this case?
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