# Rolling a Sphere around a Circle without Slipping

Rolling a Sphere around a Circle without Slipping

Consider a sphere of unit radius rolling (without spinning or slipping) around a circle of radius in the plane. The sphere's orientation can be described by a rotation about the circle center and a rotation about an axis from the sphere center to the circle center. For what angles along the circle is ? For what values of will the sphere periodically return to its initial configuration (position and orientation)?

R

θ

ϕ

θ

ϕ=0

R