# Axes Transformations

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

Axes transformation functions support transformations such as those between:

• Direction cosine matrices and quaternions

• Rotation angles and quaternions

• Earth-centered inertial (ECI) coordinates and azimuth or geodetic latitude, longitude, altitude (LLA) coordinates

• Flat Earth positions from geodetic latitude, longitude, and altitude

## 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
 `angle2dcm` Convert rotation angles to direction cosine matrix `dcm2alphabeta` Convert direction cosine matrix to angle of attack and sideslip angle `dcm2angle` Create rotation angles from direction cosine matrix `dcm2latlon` Convert direction cosine matrix to geodetic latitude and longitude `dcm2quat` Convert direction cosine matrix to quaternion `dcm2rod` Convert direction cosine matrix to Euler-Rodrigues vector `dcmbody2wind` Convert angle of attack and sideslip angle to direction cosine matrix `dcmecef2ned` Convert geodetic latitude and longitude to direction cosine matrix `dcmeci2ecef` Convert Earth-centered inertial (ECI) to Earth-centered Earth-fixed (ECEF) coordinates `quat2dcm` Convert quaternion to direction cosine matrix `rod2dcm` Convert Euler-Rodrigues vector to direction cosine matrix
 `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 `flat2lla` Convert from flat Earth position to array of geodetic coordinates `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 `lla2flat` Convert from geodetic latitude, longitude, and altitude to flat Earth position
 `geoc2geod` Convert geocentric latitude to geodetic latitude `geod2geoc` Convert geodetic latitude to geocentric latitude
 `angle2quat` Convert rotation angles to quaternion `dcm2quat` Convert direction cosine matrix to quaternion `quat2angle` Convert quaternion to rotation angles `quat2dcm` Convert quaternion to direction cosine matrix `quat2rod` Convert quaternion to Euler-Rodrigues vector `rod2quat` Convert Euler-Rodrigues vector to quaternion
 `eci2aer` Convert Earth-centered inertial (ECI) coordinates to azimuth, elevation, slant range (AER) coordinates
 `angle2rod` Convert rotation angles to Euler-Rodrigues vector `dcm2rod` Convert direction cosine matrix to Euler-Rodrigues vector `quat2rod` Convert quaternion to Euler-Rodrigues vector `rod2angle` Convert Euler-Rodrigues vector to rotation angles `rod2dcm` Convert Euler-Rodrigues vector to direction cosine matrix `rod2quat` Convert Euler-Rodrigues vector to quaternion

## Topics

Fundamental Coordinate System Concepts

Define coordinate systems when working with the Aerospace Toolbox software.

Coordinate Systems for Modeling

Define coordinate systems when modeling with the Aerospace Toolbox software.

Define coordinate systems for navigation when modeling with the Aerospace Toolbox software.

Coordinate Systems for Display

Define coordinate systems for display with the Aerospace Toolbox software.

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