Question: (a) Using Euler angles, write the constraint of rolling without slipping for a sphere of radius (R) moving on a flat surface. (b) Write the

(a) Using Euler angles, write the constraint of rolling without slipping for a sphere of radius \(R\) moving on a flat surface.

(b) Write the Lagrangian and equations of motion using Lagrange multipliers.

(c) Show that the rotational and translational kinetic energies are independently conserved.

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