# Rotation2D/3D

Rotation[bnum] returns the angle of rotation (2D) or the angle and axis of rotation (3D) of body bnum.
Rotation[{ei, ej}] (2D) or Rotation[{eo, ei, ej, ek}] (3D) returns the angle-axis of rotation associated with the given Euler parameters.
Rotation[matrix] returns the angle or angle-axis of rotation associated with the given 2D or 3D rotation matrix.

• In Modeler2D, Rotation returns scalar angle of rotation .
• In Modeler3D, Rotation returns the angle-axis of rotation in the form: {, {x, y, z}}.
• In Modeler2D, if the
Euler solution method is specified with SetSymbols, Rotation[bnum] returns the angle of rotation in terms of Euler parameters. With the Angular solution method Rotation[bnum] simply returns bnum.
• In Modeler3D, Rotation[{, vector}] returns the given angle-axis after potentially normalizing the axis and transforming it to the global reference frame.
• In Modeler3D, Rotation[vector] returns the angle-axis of rotation associated with the given virtual rotation vector.
• When Rotation is used to transform a virtual rotation or an angle-axis, vector may be a simple vector or a Mech vector object with head Vector, Line, or Plane.
• In Modeler3D, the Normalized option can be given to determine whether the resulting axis of rotation is normalized. The default setting is Normalized->True.
• With Normalized->True an Indeterminate result is returned for the axis of rotation if the angle of rotation is zero.
• See also: Alpha, Angle, EulerParameters, Omega, Origin, RotationMatrix, VirtualRotation.

Load the Modeler2D package.

Here is the rotation angle of body 2.

If we switch to Euler coordinates then the rotation angle is expressed in terms of Euler parameters.

Rotation can be used to change other representations of rotation--Euler parameters or a rotation matrix--into a rotation angle.

Load the Modeler3D package.

Here are the angle and axis or rotation of body 2 expressed in terms of Euler parameters.

Rotation can be used to change Euler parameters, a rotation matrix, or a virtual rotation vector into a rotation angle.