Lecture L3 -Vectors, Matrices and Coordinate Transformations

using vectors and defining appropriate operations between them, physical laws can often be written in a simple form. Since we will making extensive use of vectors in Dynamics, we will summarize some of their important properties.

Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering.

A concept of vector angle has not been introduced in mechanics up till now. Rotation in a fixed plane is described in terms of antisymmetric tensor or vector product. Three-dimensional rotation is described with the help of Euler’s angles [1]. But in addition to its bulkiness this method meets some principal problems: necessity to use only “small angles” and these angles’ noncommutativity. As these authors believes a concept of vector angle deprived of these problems is proposed in this article.

This note briefly explains vectors suited for Cambridge AS and A-level mathematics, Cambridge IGCSE additional mathematics, and analysis and approaches mathematics for IB Diploma Programme.