8.2 Inertial coordinate systems

The inertial system is a right-handed coordinate system according to ISO 8855 [6] with the axes pointing to the following directions (see Figure 11):

  • x ⇒ right

  • y ⇒ up

  • z ⇒ coming out of drawing plane

For geographic reference, the following convention applies:

  • x ⇒ east

  • y ⇒ north

  • z ⇒ up

Elements like objects and signals can be placed within the inertial coordinate system by applying a heading, followed by pitch, followed by roll:

img
Figure 11. Inertial coordinate system with defined rotations

Figure 11 shows the positive axes and positive directions of the corresponding angles.

heading
heading = 0.0:
heading = +π/2:

around z-axis, where
x’ points into direction of x-axis / east
x’ points into direction of y-axis / north

pitch
pitch = 0.0:
pitch = +π/2:

around y’-axis, where
x’’/y’’ plane = x’/y’ plane
direction x’’ = - z’ = -z

roll
roll = 0.0:
roll = +π/2:

around x’’-axis, where
x’’’/y’’’ plane = x’’/y’’ plane
direction z’’’ = - y’’
img
Figure 12. Inertial coordinate system with defined rotations

Figure 12 shows the different states of an inertial coordinate system with defined rotations. x’/y’/(z’=z) denotes the coordinate system after rotating x/y/z with the heading angle around the z-axis. The coordinate system x’’/(y’’=y’)/z’’ denotes the coordinate system after rotating x’/y’/z’ with the pitch angle around the y’-axis. The final rotated coordinate system (x’’’=x’’)/y’’’/z’’’ is obtained after rotating system x’’/y’’/z’’ with roll angle.