ballistics Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially weapon munitions such as bullets, unguided bombs, rockets and the like; the science or art of designing and acceler ...

and

flight dynamics Flight dynamics in aviation and spacecraft, is the study of the performance, stability, and control of vehicles flight, flying through the air or in outer space. It is concerned with how forces acting on the vehicle determine its velocity and at ...

, axes conventions are standardized ways of establishing the location and orientation of

coordinate axes In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...

for use as a

frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system, whose origin (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale have been specified in physical space. It ...

. 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

orientation Orientation may refer to: Positioning in physical space * Map orientation, the relationship between directions on a map and compass directions * Orientation (housing), the position of a building with respect to the sun, a concept in building des ...

s 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

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 DIN or Din or din may refer to: People and language * Din (name), people with the name * Dīn, an Arabic word with three general senses: judgment, custom, and religion from which the name originates * Dinka language (ISO 639 code: din), spoken ...

9300 norm for aircraft (adopted by ISO as ISO 1151–2:1985).

Earth bounded axes conventions

World reference frames: ENU and NED

Basically, as lab frame or reference frame, there are two kinds of conventions for the frames: *East, North, Up (ENU), used in geography *North, East, Down (NED), used specially in aerospace This frame referenced w.r.t. Global Reference frames like Earth Center Earth Fixed (ECEF) non-inertial system.

World reference frames for attitude description

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 The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189� ...

) the convention used should also be stated. Nevertheless, most used notations (matrices and quaternions) are unambiguous. ECEF ENU Longitude Latitude relationships

ECEF ENU Longitude Latitude relationships

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: * In case of land vehicles like cars, tanks etc., which use the ENU-system (East-North-Up) as external reference (''World frame''), the vehicle's (body's) positive ''y''- or pitch axis always points to its left, and the positive ''z''- or yaw axis always points up. World frame's origin is fixed at the center of gravity of the vehicle. * By contrast, in case of air and sea vehicles like submarines, ships, airplanes etc., which use the NED-system (North-East-Down) as external reference (''World frame''), the vehicle's (body's) positive ''y''- or pitch axis always points to its right, and its positive ''z''- or yaw axis always points down. World frame's origin is fixed at the center of gravity of the vehicle. * Finally, in case of space vehicles like the

Space Shuttle The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. ...

etc., a modification of the latter convention is used, where the vehicle's (body's) positive ''y''- or pitch axis again always points to its right, and its positive z- or yaw axis always points down, but “down” now may have two different meanings: If a so-called ''local frame'' is used as external reference, its positive z-axis points “down” to the center of the Earth as it does in case of the earlier mentioned NED-system, but if the ''inertial frame'' is used as reference, its positive z-axis will point now to the north celestial pole, and its positive x-axis to the Vernal

Equinox A solar equinox is a moment in time when the Sun appears directly above the equator, rather than to its north or south. On the day of the equinox, the Sun appears to rise directly east and set directly west. This occurs twice each year, arou ...

or some other reference meridian.

Frames mounted on vehicles

Specially for aircraft, these frames do not need to agree with the earth-bound frames in the up-down line. It must be agreed what ENU and NED mean in this context.

Conventions for land vehicles

For land vehicles it is rare to describe their complete orientation, except when speaking about

electronic stability control Electronic stability control (ESC), also referred to as electronic stability program (ESP) or dynamic stability control (DSC), is a computerized technology that improves a car handling, vehicle's stability by detecting and reducing loss of Tract ...

satellite navigation A satellite navigation or satnav system is a system that uses satellites to provide autonomous geopositioning. A satellite navigation system with global coverage is termed global navigation satellite system (GNSS). , four global systems are ope ...

. In this case, the convention is normally the one of the adjacent drawing, where RPY stands for roll-pitch-yaw.

Conventions for sea vehicles

As well as aircraft, the same terminology is used for the motion of ships and boats. Some words commonly used were introduced in maritime navigation. For example, the ''yaw'' angle or heading, has a

nautical Seamanship is the art, competence, and knowledge of operating a ship, boat or other craft on water. The'' Oxford Dictionary'' states that seamanship is "The skill, techniques, or practice of handling a ship or boat at sea." It involves topic ...

origin, with the meaning of "bending out of the course". Etymologically, it is related with the verb 'to go'. It is related to the concept of bearing. It is typically assigned the shorthand notation .

Conventions for aircraft local reference frames

Coordinates to describe an aircraft attitude (Heading, Elevation and Bank) are normally given relative to a reference control frame located in a control tower, and therefore ENU, relative to the position of the control tower on the earth surface. Coordinates to describe observations made from an aircraft are normally given relative to its intrinsic axes, but normally using as positive the coordinate pointing downwards, where the interesting points are located. Therefore, they are normally NED. These axes are normally taken so that X axis is the longitudinal axis pointing ahead, Z axis is the vertical axis pointing downwards, and the Y axis is the lateral one, pointing in such a way that the frame is

right-handed In human biology, handedness is an individual's preferential use of one hand, known as the dominant hand, due to and causing it to be stronger, faster or more Fine motor skill, dextrous. The other hand, comparatively often the weaker, less dext ...

. The ''motion'' of an aircraft is often described in terms of rotation about these axes, so rotation about the ''X''-axis is called rolling, rotation about the ''Y''-axis is called pitching, and rotation about the ''Z''-axis is called yawing.

Frames for space navigation

For satellites orbiting the Earth it is normal to use the

Equatorial coordinate system The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of astronomical object, celestial objects. It may be implemented in spherical coordinate system, spherical or Cartesian coordinate system, rect ...

. The projection of the Earth's equator onto the celestial sphere is called the

celestial equator The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. Due to Earth's axial tilt, the celestial ...

. Similarly, the projections of the Earth's north and south geographic poles become the north and south

celestial pole The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at ...

s, respectively. Deep space satellites use other

Celestial coordinate system In astronomy, coordinate systems are used for specifying positions of celestial objects (satellites, planets, stars, galaxies, etc.) relative to a given reference frame, based on physical reference points available to a situated observer (e. ...

, like the

Ecliptic coordinate system In astronomy, the ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets (except Mercury) and many small So ...

Local conventions for space ships as satellites

{{multiple image , image1 = RPY angles of spaceships (local frame).png , width1 = 180 , image2 = RPY angles of spaceships (inertial frame).png , width2 = 200 , footer = RPY angles of the Space Shuttle and other space vehicles, first using a local frame as reference and second using an inertial frame as reference. If the goal is to keep the shuttle during its orbits in a constant attitude with respect to the sky, e.g. in order to perform certain astronomical observations, the preferred reference is the ''inertial frame'', and the RPY angle vector (0, 0, 0) describes an attitude then, where the shuttle's wings are kept permanently parallel to the Earth's equator, its nose points permanently to the vernal

equinox A solar equinox is a moment in time when the Sun appears directly above the equator, rather than to its north or south. On the day of the equinox, the Sun appears to rise directly east and set directly west. This occurs twice each year, arou ...

, and its belly towards the northern polar star (see picture). (Note that rockets and missiles more commonly follow the conventions for aircraft where the RPY angle vector (0, 0, 0) points north, rather than toward the vernal equinox). On the other hand, if the goal is to keep the shuttle during its orbits in a constant attitude with respect to the surface of the Earth, the preferred reference will be the ''local frame'', with the RPY angle vector (0, 0, 0) describing an attitude where the shuttle's wings are parallel to the Earth's surface, its nose points to its heading, and its belly down towards the centre of the Earth (see picture).

Frames used to describe attitudes

Normally the frames used to describe a vehicle's local observations are the same frames used to describe its attitude with respect to the ground tracking stations. i.e. if an ENU frame is used in a tracking station, also ENU frames are used onboard and these frames are also used to refer local observations. An important case in which this does not apply is aircraft. Aircraft observations are performed downwards and therefore normally NED axes convention applies. Nevertheless, when attitudes with respect to ground stations are given, a relationship between the local earth-bound frame and the onboard ENU frame is used.

References

Euclidean symmetries Rotation in three dimensions