Mambo Toolbox Functions


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FindRotation — Extraction of relative orientation of triads [mathematica]

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

Calling Sequence

FindRotation[a1,a2]

Parameters

a1, a2: names of defined triads

Description

The function FindRotation returns the rotation matrix between the triads labeled by a1 and a2.

Examples

Restart;
DeclareTriads[a,b];
DefineTriads[a,b,q,1,2,3];
FindRotation[a,b]

${{\frac{1}{14} (1 - Cos [q]) + Cos [q], \frac{1}{7} (1 - Cos [q]) - \frac{3 Sin [q]}{\sqrt{14}}, \frac{3}{14} (1 - Cos [q]) + \sqrt{\frac{2}{7}} Sin [q]}, {\frac{1}{7} (1 - Cos [q]) + \frac{3 Sin [q]}{\sqrt{14}}, \frac{2}{7} (1 - Cos [q]) + Cos [q], \frac{3}{7} (1 - Cos [q]) - \frac{Sin [q]}{\sqrt{14}}}, {\frac{3}{14} (1 - Cos [q]) - \sqrt{\frac{2}{7}} Sin [q], \frac{3}{7} (1 - Cos [q]) + \frac{Sin [q]}{\sqrt{14}}, \frac{9}{14} (1 - Cos [q]) + Cos [q]}}$

Toolbox functions

AngularMomentum AngularVelocity Boolean Expressions CoeffExtract DeclareObservers DeclarePoints DeclareStates DeclareTriads DefineNeighbors DefineObjects DefineObservers DefinePoints DefineTriads DiffTime FindCoordinates FindOrientation FindPosition FindRotation FindTranslation ForceDescription GeometryOutput LinearMomentum LinearVelocity MakeDescription MakeRotations MakeTranslations MamboCross MamboDot MamboExpress MamboMinus MamboNorm MamboPlus MamboSimplify MamboTimes MomentumDescription MotionOutput NullVector Restart SetTime Undo VelocityDescription