This information is part of the Modelica Standard Library maintained by the Modelica Association.

# Frames

Functions to transform rotational frame quantities

## Package Contents

Internal Internal definitions that may be removed or changed (do not use) | |

Quaternions Functions to transform rotational frame quantities based on quaternions (also called Euler parameters) | |

TransformationMatrices Functions for transformation matrices | |

absoluteRotation Return absolute orientation object from another absolute and a relative orientation object | |

angularVelocity1 Return angular velocity resolved in frame 1 from orientation object | |

angularVelocity2 Return angular velocity resolved in frame 2 from orientation object | |

axesRotations Return fixed rotation object to rotate in sequence around fixed angles along 3 axes | |

axesRotationsAngles Return the 3 angles to rotate in sequence around 3 axes to construct the given orientation object | |

axis Return unit vector for x-, y-, or z-axis | |

axisRotation Return rotation object to rotate around an angle along one frame axis | |

from_nxy Return fixed orientation object from n_x and n_y vectors | |

from_nxz Return fixed orientation object from n_x and n_z vectors | |

from_Q Return orientation object R from quaternion orientation object Q | |

from_T Return orientation object R from transformation matrix T | |

from_T_inv Return orientation object R from inverse transformation matrix T_inv | |

from_T2 Return orientation object R from transformation matrix T and its derivative der(T) | |

inverseRotation Return inverse orientation object | |

nullRotation Return orientation object that does not rotate a frame | |

Orientation Orientation object defining rotation from a frame 1 into a frame 2 | |

orientationConstraint Return residues of orientation constraints (shall be zero) | |

planarRotation Return orientation object of a planar rotation | |

planarRotationAngle Return angle of a planar rotation, given the rotation axis and the representations of a vector in frame 1 and frame 2 | |

relativeRotation Return relative orientation object | |

resolve1 Transform vector from frame 2 to frame 1 | |

resolve2 Transform vector from frame 1 to frame 2 | |

resolveDyade1 Transform second order tensor from frame 2 to frame 1 | |

resolveDyade2 Transform second order tensor from frame 1 to frame 2 | |

resolveRelative Transform vector from frame 1 to frame 2 using absolute orientation objects of frame 1 and of frame 2 | |

smallRotation Return rotation angles valid for a small rotation and optionally residues that should be zero | |

to_exy Map rotation object into e_x and e_y vectors of frame 2, resolved in frame 1 | |

to_Q Return quaternion orientation object Q from orientation object R | |

to_T Return transformation matrix T from orientation object R | |

to_T_inv Return inverse transformation matrix T_inv from orientation object R | |

to_vector Map rotation object into vector |