Say I have a position vector
p = e(t) p(t)
Where, in 2D, e(t) = (e1(t), e2(t)) and p(t) = (p1(t), p2(t))T
And if I conveniently point the FIRST base vector of the frame at the particle, I can use: p(t) = (r1(t), 0)T
I want the velocity, so I take
v = d(e(t))/dt p(t) + e(t) d(p(t))/dt...