SphericalCoords Class Reference

Three mobilities -- body fixed 3-2 (z-y) rotation followed by translation along body z or body x. More...

#include <MobilizedBody.h>

Inheritance diagram for SphericalCoords:

Public Member Functions
	SphericalCoords (Direction=Forward)
	SphericalCoords (MobilizedBody &parent, const Body &, Direction=Forward)
	By default the parent body frame and the body's own frame are used as the inboard and outboard mobilizer frames, resp.
	SphericalCoords (MobilizedBody &parent, const Transform &inbFrame, const Body &, const Transform &outbFrame, Direction=Forward)
	Use this constructor to specify mobilizer frames which are not coincident with the body frames.
	SphericalCoords (MobilizedBody &parent, const Transform &inbFrame, const Body &, const Transform &outbFrame, Real azimuthOffset, bool azimuthNegated, Real zenithOffset, bool zenithNegated, CoordinateAxis radialAxis, bool radialNegated, Direction=Forward)
	Use this constructor to specify the general case described above.
SphericalCoords &	addBodyDecoration (const Transform &X_BD, const DecorativeGeometry &g)
	Add decorative geometry specified relative to the new (outboard) body's reference frame B, or to the outboard mobilizer frame M attached to body B, or to the inboard mobilizer frame F attached to the parent body P.
SphericalCoords &	addOutboardDecoration (const Transform &X_MD, const DecorativeGeometry &g)
	Add decorative geometry specified relative to the outboard mobilizer frame M attached to body B.
SphericalCoords &	addInboardDecoration (const Transform &X_FD, const DecorativeGeometry &g)
	Add decorative geometry specified relative to the inboard mobilizer frame F attached to the parent body P.
SphericalCoords &	setDefaultInboardFrame (const Transform &X_PF)
	Change this mobilizer's frame F on the parent body P.
SphericalCoords &	setDefaultOutboardFrame (const Transform &X_BM)
	Change this mobilizer's frame M fixed on this (the outboard) body B.
SphericalCoords &	setDefaultAngles (const Vec2 &a)
SphericalCoords &	setDefaultRadius (Real r)
SphericalCoords &	setRadialAxis (CoordinateAxis)
SphericalCoords &	setNegateAzimuth (bool)
SphericalCoords &	setNegateZenith (bool)
SphericalCoords &	setNegateRadial (bool)
const Vec2 &	getDefaultAngles () const
Real	getDefaultTranslation () const
CoordinateAxis	getRadialAxis () const
bool	isAzimuthNegated () const
bool	isZenithNegated () const
bool	isRadialNegated () const
void	setAngles (State &s, const Vec2 &a)
void	setRadius (State &s, Real r)
const Vec2 &	getAngles (const State &s) const
Real	getRadius (const State &s) const
const Vec3 &	getDefaultQ () const
SphericalCoords &	setDefaultQ (const Vec3 &q)
const Vec3 &	getQ (const State &) const
const Vec3 &	getQDot (const State &) const
const Vec3 &	getQDotDot (const State &) const
const Vec3 &	getU (const State &) const
const Vec3 &	getUDot (const State &) const
void	setQ (State &, const Vec3 &) const
void	setU (State &, const Vec3 &) const
const Vec3 &	getMyPartQ (const State &, const Vector &qlike) const
const Vec3 &	getMyPartU (const State &, const Vector &ulike) const
Vec3 &	updMyPartQ (const State &, Vector &qlike) const
Vec3 &	updMyPartU (const State &, Vector &ulike) const
	SimTK_INSERT_DERIVED_HANDLE_DECLARATIONS (SphericalCoords, SphericalCoordsImpl, MobilizedBody)

Detailed Description

Three mobilities -- body fixed 3-2 (z-y) rotation followed by translation along body z or body x.

Interpreted as spherical coordinates the first rotation is the azimuth angle, the second is the zenith, and the translation is the radius. We permit a simple mapping from generalized coordinates to (azimuth, zenith, radius):

     azimuth = s0*q0 + az0   (about Fz==Mz)
     zenith  = s1*q1 + ze0   (about My)
     radius  = s2*q2         (along Mz or Mx; Mz is default)

where s0,s1,s2 are signs (1 or -1) and az0 and ze0 are offset angles. The F and M frames are coincident when azimuth==zenith==radius==0. But note that with non-zero offsets the F and M frames will not be aligned in the reference configuration where q0==q1==q2==0. The F and M origins will always be coincident when q2==0, however.

This mobilizer can be used to give unrestricted 3-d motion to inertialess particles (as with a Cartesian mobilizer but parameterized torsion,bend,stretch instead of x,y,z) but in this case you must watch for two possible singularities: (1) radius==0, and (2) zenith==n*Pi (or equivalently q1==n*Pi-s1*ze0). If your operating range steers clear of those singularities, you're fine.

Constructor & Destructor Documentation

SphericalCoords ( Direction = Forward ) [explicit]

SphericalCoords	(	MobilizedBody &	parent,
		const Body &	,
		Direction	= `Forward`
	)

By default the parent body frame and the body's own frame are used as the inboard and outboard mobilizer frames, resp.

SphericalCoords	(	MobilizedBody &	parent,
		const Transform &	inbFrame,
		const Body &	,
		const Transform &	outbFrame,
		Direction	= `Forward`
	)

Use this constructor to specify mobilizer frames which are not coincident with the body frames.

This gives you a pure spherical coordinate system in which q0=azimuth about Fz(==Mz), q1=zenith about My, and q2=radius along Mz.

SphericalCoords	(	MobilizedBody &	parent,
		const Transform &	inbFrame,
		const Body &	,
		const Transform &	outbFrame,
		Real	azimuthOffset,
		bool	azimuthNegated,
		Real	zenithOffset,
		bool	zenithNegated,
		CoordinateAxis	radialAxis,
		bool	radialNegated,
		Direction	= `Forward`
	)

Use this constructor to specify the general case described above.

Member Function Documentation

SphericalCoords& addBodyDecoration	(	const Transform &	X_BD,
		const DecorativeGeometry &	g
	)			`[inline]`

Add decorative geometry specified relative to the new (outboard) body's reference frame B, or to the outboard mobilizer frame M attached to body B, or to the inboard mobilizer frame F attached to the parent body P.

Note that the body itself may already have had some decorative geometry on it when it was first put into this MobilizedBody; in that case this just adds more.

Reimplemented from MobilizedBody.

References MobilizedBody::addBodyDecoration().

SphericalCoords& addInboardDecoration	(	const Transform &	X_FD,
		const DecorativeGeometry &
	)			`[inline]`

Add decorative geometry specified relative to the inboard mobilizer frame F attached to the parent body P.

If body P already has decorative geometry on it, this just adds some more.

Reimplemented from MobilizedBody.

References MobilizedBody::addInboardDecoration().

SphericalCoords& addOutboardDecoration	(	const Transform &	X_MD,
		const DecorativeGeometry &
	)			`[inline]`

Add decorative geometry specified relative to the outboard mobilizer frame M attached to body B.

If body B already has decorative geometry on it, this just adds some more.

Reimplemented from MobilizedBody.

References MobilizedBody::addOutboardDecoration().

const Vec2& getAngles ( const State & s ) const [inline]

References Vec< M, ELT, STRIDE >::getSubVec().

const Vec2& getDefaultAngles ( ) const [inline]

References Vec< M, ELT, STRIDE >::getSubVec().

const Vec3& getDefaultQ ( ) const

Real getDefaultTranslation ( ) const [inline]

const Vec3& getMyPartQ	(	const State &	,
		const Vector &	qlike
	)			const

const Vec3& getMyPartU	(	const State &	,
		const Vector &	ulike
	)			const

const Vec3& getQ ( const State & ) const

const Vec3& getQDot ( const State & ) const

const Vec3& getQDotDot ( const State & ) const

CoordinateAxis getRadialAxis ( ) const

Real getRadius ( const State & s ) const [inline]

const Vec3& getU ( const State & ) const

const Vec3& getUDot ( const State & ) const

bool isAzimuthNegated ( ) const

bool isRadialNegated ( ) const

bool isZenithNegated ( ) const

void setAngles	(	State &	s,
		const Vec2 &	a
	)			`[inline]`

SphericalCoords& setDefaultAngles ( const Vec2 & a ) [inline]

References Vec< M, ELT, STRIDE >::updSubVec().

SphericalCoords& setDefaultInboardFrame ( const Transform & X_PF ) [inline]

Change this mobilizer's frame F on the parent body P.

Calling this method invalidates the MobilizedBody's topology, so the containing matter subsystem's realizeTopology() method must be called again. A reference to this MobilizedBody is returned so that this can be chained like an assignment operator.

Reimplemented from MobilizedBody.

References MobilizedBody::setDefaultInboardFrame().

SphericalCoords& setDefaultOutboardFrame ( const Transform & X_BM ) [inline]

Change this mobilizer's frame M fixed on this (the outboard) body B.

Calling this method invalidates the MobilizedBody's topology, so the containing matter subsystem's realizeTopology() method must be called again. A reference to this MobilizedBody is returned so that this can be chained like an assignment operator.

Reimplemented from MobilizedBody.

References MobilizedBody::setDefaultOutboardFrame().

SphericalCoords& setDefaultQ ( const Vec3 & q )

SphericalCoords& setDefaultRadius ( Real r ) [inline]

SphericalCoords& setNegateAzimuth ( bool )

SphericalCoords& setNegateRadial ( bool )

SphericalCoords& setNegateZenith ( bool )

void setQ	(	State &	,
		const Vec3 &
	)			const

SphericalCoords& setRadialAxis ( CoordinateAxis )

void setRadius	(	State &	s,
		Real	r
	)			`[inline]`

void setU	(	State &	,
		const Vec3 &
	)			const

SimTK_INSERT_DERIVED_HANDLE_DECLARATIONS	(	SphericalCoords	,
		SphericalCoordsImpl	,
		MobilizedBody
	)

Vec3& updMyPartQ	(	const State &	,
		Vector &	qlike
	)			const

Vec3& updMyPartU	(	const State &	,
		Vector &	ulike
	)			const

The documentation for this class was generated from the following file:

MobilizedBody.h

SphericalCoords Class Reference

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation