Rigid Body Dynamics $-$ Marble Rolling on a Circular Surface

Determine the EOM for a sphere object of radius $\backslash ($ r $\backslash )$ and mass $\backslash ($ m $\backslash )$ rolling on a circular crosssection of radius $\backslash ($ R $\backslash ).$

The center of mass is moving in a circular path relative to the center of the circular surface. Its center of mass has an angular position $\backslash (\backslash$theta $\backslash )$ relative to vertical going through the center of the circular cross$-$section but the angular rotation of the sphere relative to a vertical through its center of mass is $\backslash (\backslash$beta $\backslash ).$

Sum forces using polar or normal$-$tangential coordinates. Sum moments where the angular acceleration of the sphere is the acceleration of $\backslash (\backslash$beta $\backslash ).$ Use a rolling without slipping constraint.

Determine the equation for acceleration of $\backslash (\backslash$theta $\backslash ),$ the EOM of the problem.