# Thornton & Marion, Classical Dynamics, 5th Edition

## Chapter 1. Matrices, Vectors, and Vector Calculus

### Problem 03. Transformation Matrix

#### The problem asks you to

- find a transformation matrix that satisfying some conditions.

#### This problem gives (or assumes)

- This matrix rotates a rectangular coordinate through an angle of 120 degrees about an axis making equal angles with the original one.

#### You should know about

- Direction cosine
- Transformation matrix

#### Solution

We can see the relation between the rotated and the original coordinates system. This picture shows that

So, the transformation matrix is

Therefore,