Frenet and Curlicue
If K(t) is a function in a Lie algebra then the Frenet equations Q'(t)=K(t) Q(t), Q(0)=1 defines a path in the corresponding Lie group. We can now use K(t) to define the Frenet path using the equation R'(t)=Q(t). This defines r(t), where r'(t) is the first row of R(t). The …