Thornton & Marion, Classical Dynamics, Fifth Edition

Chapter 1. Matrices, Vectors, and Vector Calculus

Problem 10. Differentiation of a vector

calculate vector derivatives to get velocity and acceleration of a particle.
position vector of a particle in a plain elliptical orbit.
$\bold{r} = 2b \sin \omega t \bold{i} + b \cos \omega t \bold{j}$
calculation of vector derivatives.