Further, one can also express the EOMs in Eq. 102 directly in terms of the generalized Euler angles {θ n , ϕ n }, without using the conjugated variables {Θ n , ϕ n }. To this end, we use the expression of Θ n ({θ k }) in Eq. 74 and directly work out its time derivative (through the chain rule with θ n ) as follows