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EulerParameters
2D/3D

EulerParameters[bnum] returns the Euler parameters {ei, ej} (2D) or {eo, ei, ej, ek} (3D) associated with body bnum.
EulerParameters[{ang}] (2D) or EulerParameters[{ang, vector}] (3D) returns Euler parameters associated with ang or ang and vector.
EulerParameters[matrix] returns the Euler parameters associated with the given 2D or 3D rotation matrix.

• In Modeler2D, if the Angular solution method is specified with SetSymbols, EulerParameters returns the parameters in terms of the body's rotation angle. With the Euler solution method EulerParameters simply returns {Eibnum, Ejbnum}.
• Degenerate 2D Euler parameters are defined as  in terms of a given angle ang.
• Euler parameters are defined as  , and  in terms of an angle and axis of rotation.
• When transforming a rotation, {ang, vector}, the Assumptions->Normalized option may be given to cause EulerParameters to assume that vector is a unit vector, thus simplifying the result. The default setting is Assumptions->None.
• In Modeler3D, EulerParameters[vector] returns the four Euler parameters associated with the given virtual rotation vector.
• When EulerParameters 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.
• See also: Rotation, RotationMatrix, VirtualRotation.

Further Examples

Load the Modeler3D package.

Here are the Euler parameters for body 2.

Here are the Euler parameters representing a rotation of Pi/2 about the X axis.

Here are the Euler parameters generally representing a rotation about an axis.


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