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Euler
2D/3D

Euler is a setting for the Method option for SetSymbols that causes all subsequently built models to use Euler parameters and their derivatives to represent angular orientation and velocity.

• The alternative to the Euler setting is Angular.
• In Modeler2D, the Euler solution method causes the angular orientation of a body to be represented by two parameters ei and ej, which are related to the single angular coordinate CapitalTheta by ei = cos(CapitalTheta) and ej = sin(CapitalTheta). The angular velocity and acceleration are also represented by pairs of parameters, eind, ejnd and eindd, ejndd.
• In Modeler3D, the angular orientation of a body is always represented by four Euler parameters, and with the Euler solution method the angular velocity and acceleration are also represented by derivatives of the Euler parameters.
• See also: EulerParameters, Rotation.

Further Examples

Load the Modeler2D package and define a simple model.

The default solution method for 2D models is Angular so the results given by SolveMech are in terms of angular coordinates CapitalTheta2, CapitalTheta3, ....

If we change the solution method to Euler then the same results are expressed in terms of Euler parameters.

Load the Modeler3D package and define a simple model.

For 3D models, the default solution method is Euler so the angular orientation and angular velocity of each body are given in terms of Euler parameters and their derivatives.

If we change the solution method to Angular, then the angular velocity is expressed in terms of the components of the angular velocity vector.

However, if we want the derivatives of the Euler parameters, they can still be obtained in terms of the angular velocity terms.

See HelpModel2D, HelpModel3D.


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