Next: Problems Up: Introduction Previous: Mathematical Notation

Coordinate Systems and Frames of Reference

The location of a point on a line can be described by one coordinate; a point on a plane can be described by two coordinates; a point in a three dimensional volume can be described by three coordinates. In general, the number of coordinates equals the number of dimensions. A coordinate system consists of:

1.: a fixed reference point (origin)
2.: a set of axes with specified directions and scales
3.: instructions that specify how to label a point in space relative to the origin and axes.

For Example:

Cartesian coordinate system (rectangular coordinate system): (x,y)

Figure 2.1: Cartesian coordinate system
$\begin{figure} \begin{center} \leavevmode \epsfxsize=4 cm \epsfbox{fig11.eps}\end{center}\end{figure}$
Plane polar coordinates: (r, $\theta$ )

Figure 2.2: Plane polar coordinates
$\begin{figure} \begin{center} \leavevmode \epsfxsize=4 cm \epsfbox{fig12.eps}\end{center}\end{figure}$

**Figure 2.1:** Cartesian coordinate system
$\begin{figure} \begin{center} \leavevmode \epsfxsize=4 cm \epsfbox{fig11.eps}\end{center}\end{figure}$

**Figure 2.2:** Plane polar coordinates
$\begin{figure} \begin{center} \leavevmode \epsfxsize=4 cm \epsfbox{fig12.eps}\end{center}\end{figure}$

Definition: The position vector ( $\vec{r}$ ) in any given coordinate system specifys the position of a given point within that coordinate system relative to the origin.

www-admin@theory.uwinnipeg.ca
10/9/1997