# Axes Transformations

Coordinate axes transformations, such as Euler angles to quaternions and Euler-Rodrigues angles to quaternions

Axes transformation functions support transformations such as:

• Conversions between different rotation representations, such as those between Direction cosine matrices (DCM), quaternions, rotation angles, and Euler-Rodrigues angles

• Coordinate system transformation between common aerospace coordinate systems defined with respect to the center or surface of Earth, such as ECI, ECEF, NED, Flat Earth

• Axes transformations between common aerospace body-fixed coordinate system, such as Body, Wind, and Stability axes

• Transformations between geodetic and geocentric latitude, longitude, and altitude and Cartesian coordinate frames

## Functions

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 `angle2dcm` Convert rotation angles to direction cosine matrix `angle2quat` Convert rotation angles to quaternion `angle2rod` Convert rotation angles to Euler-Rodrigues vector `rod2angle` Convert Euler-Rodrigues vector to rotation angles `quat2angle` Convert quaternion to rotation angles `rod2dcm` Convert Euler-Rodrigues vector to direction cosine matrix `dcm2angle` Create rotation angles from direction cosine matrix `dcm2quat` Convert direction cosine matrix to quaternion `dcm2rod` Convert direction cosine matrix to Euler-Rodrigues vector `quat2dcm` Convert quaternion to direction cosine matrix `quat2rod` Convert quaternion to Euler-Rodrigues vector `rod2quat` Convert Euler-Rodrigues vector to quaternion
 `dcmeci2ecef` Convert Earth-centered inertial (ECI) to Earth-centered Earth-fixed (ECEF) coordinates `dcmecef2ned` Convert geodetic latitude and longitude to direction cosine matrix `dcm2latlon` Convert direction cosine matrix to geodetic latitude and longitude `eci2ecef` Position, velocity, and acceleration vectors in Earth-centered Earth-fixed (ECEF) coordinate system `eci2lla` Convert Earth-centered inertial (ECI) coordinates to latitude, longitude, altitude (LLA) geodetic coordinates `eci2aer` Convert Earth-centered inertial (ECI) coordinates to azimuth, elevation, slant range (AER) coordinates `ecef2eci` Position and velocity vectors in Earth-centered inertial mean-equator mean-equinox `ecef2lla` Convert Earth-centered Earth-fixed (ECEF) coordinates to geodetic coordinates `lla2eci` Convert geodetic latitude, longitude, altitude (LLA) coordinates to Earth-centered inertial (ECI) coordinates `lla2ecef` Convert geodetic coordinates to Earth-centered Earth-fixed (ECEF) coordinates `flat2lla` Convert from flat Earth position to array of geodetic coordinates `lla2flat` Convert from geodetic latitude, longitude, and altitude to flat Earth position
 `dcm2alphabeta` Convert direction cosine matrix to angle of attack and sideslip angle `dcmbody2stability` Convert body frame to stability frame transformation matrix (Since R2022a) `dcmbody2wind` Convert angle of attack and sideslip angle to direction cosine matrix
 `geoc2geod` Convert geocentric latitude to geodetic latitude `geod2geoc` Convert geodetic latitude to geocentric latitude `dcm2latlon` Convert direction cosine matrix to geodetic latitude and longitude `lla2ecef` Convert geodetic coordinates to Earth-centered Earth-fixed (ECEF) coordinates `lla2eci` Convert geodetic latitude, longitude, altitude (LLA) coordinates to Earth-centered inertial (ECI) coordinates `flat2lla` Convert from flat Earth position to array of geodetic coordinates `lla2flat` Convert from geodetic latitude, longitude, and altitude to flat Earth position `ecef2lla` Convert Earth-centered Earth-fixed (ECEF) coordinates to geodetic coordinates `eci2lla` Convert Earth-centered inertial (ECI) coordinates to latitude, longitude, altitude (LLA) geodetic coordinates