Mambo Toolbox Functions

Reference: Appendix B in Multibody Mechanics and Visualization by Harry Dankowicz, published by Springer Verlag UK, 2004.

Calling Sequence

DefineTriads(a,b,rm)

DefineTriads([a1,b1,rm1], ..., [an,bn,rmn])

Parameters

a,a1, ..., an: names of declared triads

b,b1, ..., bn: names of declared triads

rm,rm1, ..., rmn: rotation-matrix specifications

Description

The function DefineTriads defines a direct relation between two declared triads by specifying the rotation matrix from the first triad to the second triad. A pair of indirectly related triads may not be defined.

The function DefineTriads results in permanent changes to the global variables GlobalTriadDeclarations and GlobalTriadDefinitions.

The syntax of a rotation-matrix specification corresponds to that of the argument to the MakeRotations procedure.

Examples

>Restart():
>DeclareTriads(a,b,c):
>DefineTriads([a,b,phi,1],[b,c,[q3,2],[Pi/2,3]]):
>print(GlobalTriadDeclarations);

$table ([b = \{a, c\}, a = \{b\}, c = \{b\}])$

>print(GlobalTriadDefinitions);

$table ([(b, a) = [\begin{array}{c} 1 & 0 & 0 \\ 0 & \cos (phi) & \sin (phi) \\ 0 & - \sin (phi) & \cos (phi) \end{array}], (c, b) = [\begin{array}{c} 0 & 1 & 0 \\ - \cos (q3) & 0 & \sin (q3) \\ \sin (q3) & 0 & \cos (q3) \end{array}], (b, c) = [\begin{array}{c} 0 & - \cos (q3) & \sin (q3) \\ 1 & 0 & 0 \\ 0 & \sin (q3) & \cos (q3) \end{array}], (a, b) = [\begin{array}{c} 1 & 0 & 0 \\ 0 & \cos (phi) & - \sin (phi) \\ 0 & \sin (phi) & \cos (phi) \end{array}]])$

Toolbox functions

&**, &++, &--, &xx, &oo &>, &>=, &<, &<=, &==, &!= AngularMomentum AngularVelocity CoeffExtract DeclareObservers DeclarePoints DeclareStates DeclareTriads DefineNeighbors DefineObjects DefineObservers DefinePoints DefineTriads DiffTime Express FindCoordinates FindOrientation FindPosition FindRotation FindTranslation ForceDescription GeometryOutput LinearMomentum LinearVelocity MakeDescription MakeRotations MakeTranslations MomentumDescription MotionOutput NullVector Restart Simplify Undo VectorLength VelocityDescription


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