Vector quantities

Introduction

The quantities available for post-processing can be scalar or vector quantities.

This section deals with vector quantities and recalls some definitions: complex notation, elliptical representation…

Vector quantities (complex notation as rotating vectors)

Each component of a vector quantity can be written as a sinusoidal quantity:

; …

or, in complex notation:

; …

; …

where:

• is the modulus of the complex component
• is the argument (or the phase) of the complex component
• is the real part of the complex component
• is the imaginary part of the complex component

Elliptical representation in 2D

In general case, the vector quantities are varying in function of time on ellipses.

For each point, the magnetic flux density can be written:

These are the parametric equations of an ellipse.

The two components of the magnetic flux density can be expressed depending on the ellipse characteristics, as follows:

• , where

• where

  a is called “½ major axis” and b is called “½ minor axis”