Axes conventions

In ballistics and flight dynamics, axes conventions are standardized ways of establishing the location and orientation of coordinate axes for use as a frame of reference. Mobile objects are normally tracked from an external frame considered fixed. Other frames can be defined on those mobile objects to deal with relative positions for other objects. Finally, attitudes or orientations can be described by a relationship between the external frame and the one defined over the mobile object.

The orientation of a vehicle is normally referred to as attitude. It is described normally by the orientation of a frame fixed in the body relative to a fixed reference frame. The attitude is described by attitude coordinates, and consists of at least three coordinates.

While from a geometrical point of view the different methods to describe orientations are defined using only some reference frames, in engineering applications it is important also to describe how these frames are attached to the lab and the body in motion.

Due to the special importance of international conventions in air vehicles, several organizations have published standards to be followed. For example, German DIN has published the DIN 9300 norm for aircraft (adopted by ISO as ISO 1151–2:1985).

Basically, as lab frame or reference frame, there are two kinds of conventions for the frames (sometimes named LVLH, local vertical, local horizontal):

These frames are location dependent. For movements around the globe, like air or sea navigation, the frames are defined as tangent to the lines of coordinates.

To establish a standard convention to describe attitudes, it is required to establish at least the axes of the reference system and the axes of the rigid body or vehicle. When an ambiguous notation system is used (such as Euler angles) also the used convention should be stated. Nevertheless, most used notations (matrices and quaternions) are unambiguous.

Tait–Bryan angles are often used to describe a vehicle's attitude with respect to a chosen reference frame, though any other notation can be used. The positive x-axis in vehicles points always in the direction of movement. For positive y- and z-axis, we have to face two different conventions:

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