Mambo Toolbox Functions - AngularMomentum


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

Reference for maple version: 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]

${Type \to Vector, Size \to 1, 1 \to {Coordinates \to {Inertia13 (Sin [q2] Sin [q3] {q1}^{'} + Cos [q3] {q2}^{'}) + Inertia12 (- Cos [q3] Sin [q2] {q1}^{'} + Sin [q3] {q2}^{'}) + Inertia11 (Cos [q2] {q1}^{'} + {q3}^{'}), Inertia23 (Sin [q2] Sin [q3] {q1}^{'} + Cos [q3] {q2}^{'}) + Inertia22 (- Cos [q3] Sin [q2] {q1}^{'} + Sin [q3] {q2}^{'}) + Inertia21 (Cos [q2] {q1}^{'} + {q3}^{'}), Inertia33 (Sin [q2] Sin [q3] {q1}^{'} + Cos [q3] {q2}^{'}) + Inertia32 (- Cos [q3] Sin [q2] {q1}^{'} + Sin [q3] {q2}^{'}) + Inertia31 (Cos [q2] {q1}^{'} + {q3}^{'})}, Triad \to b}}$

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