Mambo Toolbox Functions - AngularMomentum


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AngularMomentum — Extraction of angular momentum of rigid body relative to observer [maple]

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

Calling Sequence

AngularMomentum(A,b)

Parameters

A: name of defined observer

b: name of defined triad

Description

The function AngularMomentum returns the angular momentum of a rigid body with reference triad b relative to the observer A.

The angular momentum is expressed using the symbols Inertia11, Inertia12, and so on, to represent the components of the moment of inertia matrix.

Remember to invoke DeclareStates prior to using AngularMomentum.

Examples

>Restart(): >DeclareObservers(A): >DeclarePoints(A): >DeclareTriads(a,b): >DefineObservers([A,A,a]): >DefineTriads(a,b,[q1,1],[q2,3],[q3,1]): >DeclareStates(q1,q2,q3): >AngularMomentum(A,b);

$table ([1 = table ([Coordinates = [\begin{array}{c} Inertia11 (\cos (q2) q1t + q3t) + Inertia12 (q2t \sin (q3) - \sin (q2) q1t \cos (q3)) + Inertia13 (q2t \cos (q3) + \sin (q3) q1t \sin (q2)) \\ Inertia21 (\cos (q2) q1t + q3t) + Inertia22 (q2t \sin (q3) - \sin (q2) q1t \cos (q3)) + Inertia23 (q2t \cos (q3) + \sin (q3) q1t \sin (q2)) \\ Inertia31 (\cos (q2) q1t + q3t) + Inertia32 (q2t \sin (q3) - \sin (q2) q1t \cos (q3)) + Inertia33 (q2t \cos (q3) + \sin (q3) q1t \sin (q2)) \end{array}], Triad = b]), Size = 1, Type = Vector])$

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