lagrange mechanics on the two-sphere

 Hello Dears,
i would like to do code "Lagrange mechanics on the two-spheres" which is almost new materials and i am self-studying, so i need some guidance; i configured one arbitrary manifold such as chain of pendulums and i would like to achieve the equation motion of this system, but there is a "qi" unit-vector S^2={q E R^3 such that ||q|| = 1} which is questionary for me in updating the value and coding?
e.g :"Dynamics and Control of a Chain Pendulum on a Cart"
Thank you.