Thornton & Marion, Classical Dynamics, 5th Edition

Chapter 1. Matrices, Vectors, and Vector Calculus

Problem 10. Differentiation of a vector

• calculate vector derivatives to get the velocity and acceleration of a particle.

The problem gives

• position vector of a particle in a plain elliptical orbit.

$\bold{r} = 2b \sin \omega t \bold{i} + b \cos \omega t \bold{j}$