A class for inertial information about a rigid body consisting of the scalar mass and a 3x3 symmetric moment of inertia matrix stored as two Vector3's. More...

#include <gz/math/MassMatrix3.hh>

Public Member Functions
	MassMatrix3 ()
	Default Constructor, which inializes the mass and moments to zero. More...

	MassMatrix3 (const MassMatrix3< T > &_m)=default
	Copy constructor. More...

	MassMatrix3 (const T &_mass, const Vector3< T > &_ixxyyzz, const Vector3< T > &_ixyxzyz)
	Constructor. More...

	~MassMatrix3 ()=default
	Destructor. More...

Vector3< T >	DiagonalMoments () const
	Get the diagonal moments of inertia (Ixx, Iyy, Izz). More...

T	Epsilon (const T _tolerance=GZ_MASSMATRIX3_DEFAULT_TOLERANCE< T >) const
	Get an epsilon value that represents the amount of acceptable error in a MassMatrix3. The epsilon value is related to machine precision multiplied by the largest possible moment of inertia. More...

bool	EquivalentBox (Vector3< T > &_size, Quaternion< T > &_rot, const T _tol=1e-6) const
	Get dimensions and rotation offset of uniform box with equivalent mass and moment of inertia. To compute this, the Matrix3 is diagonalized. The eigenvalues on the diagonal and the rotation offset of the principal axes are returned. More...

bool	IsNearPositive (const T _tolerance=GZ_MASSMATRIX3_DEFAULT_TOLERANCE< T >) const
	Verify that inertia values are positive semidefinite. More...

bool	IsPositive (const T _tolerance=GZ_MASSMATRIX3_DEFAULT_TOLERANCE< T >) const
	Verify that inertia values are positive definite. More...

bool	IsValid (const T _tolerance=GZ_MASSMATRIX3_DEFAULT_TOLERANCE< T >) const
	Verify that inertia values are positive semi-definite and satisfy the triangle inequality. More...

T	Ixx () const
	Get IXX. More...

T	Ixy () const
	Get IXY. More...

T	Ixz () const
	Get IXZ. More...

T	Iyy () const
	Get IYY. More...

T	Iyz () const
	Get IYZ. More...

T	Izz () const
	Get IZZ. More...

T	Mass () const
	Get the mass. More...

Matrix3< T >	Moi () const
	returns Moments of Inertia as a Matrix3 More...

Vector3< T >	OffDiagonalMoments () const
	Get the off-diagonal moments of inertia (Ixy, Ixz, Iyz). More...

bool	operator!= (const MassMatrix3< T > &_m) const
	Inequality test operator. More...

MassMatrix3 &	operator= (const MassMatrix3< T > &_massMatrix)=default
	Equal operator. More...

bool	operator== (const MassMatrix3< T > &_m) const
	Equality comparison operator. More...

Quaternion< T >	PrincipalAxesOffset (const T _tol=1e-6) const
	Compute rotational offset of principal axes. More...

Vector3< T >	PrincipalMoments (const T _tol=1e-6) const
	Compute principal moments of inertia, which are the eigenvalues of the moment of inertia matrix. More...

bool	SetDiagonalMoments (const Vector3< T > &_ixxyyzz)
	Set the diagonal moments of inertia (Ixx, Iyy, Izz). More...

bool	SetFromBox (const Material &_mat, const Vector3< T > &_size, const Quaternion< T > &_rot=Quaternion< T >::Identity)
	Set inertial properties based on a Material and equivalent box. More...

bool	SetFromBox (const T _mass, const Vector3< T > &_size, const Quaternion< T > &_rot=Quaternion< T >::Identity)
	Set inertial properties based on mass and equivalent box. More...

bool	SetFromBox (const Vector3< T > &_size, const Quaternion< T > &_rot=Quaternion< T >::Identity)
	Set inertial properties based on equivalent box using the current mass value. More...

bool	SetFromConeZ (const Material &_mat, const T _length, const T _radius, const Quaternion< T > &_rot=Quaternion< T >::Identity)
	Set inertial properties based on a Material and equivalent cone aligned with Z axis. More...

bool	SetFromConeZ (const T _length, const T _radius, const Quaternion< T > &_rot)
	Set inertial properties based on equivalent cone aligned with Z axis using the current mass value. More...

bool	SetFromConeZ (const T _mass, const T _length, const T _radius, const Quaternion< T > &_rot=Quaternion< T >::Identity)
	Set inertial properties based on mass and equivalent cone aligned with Z axis. More...

bool	SetFromCylinderZ (const Material &_mat, const T _length, const T _radius, const Quaternion< T > &_rot=Quaternion< T >::Identity)
	Set inertial properties based on a Material and equivalent cylinder aligned with Z axis. More...

bool	SetFromCylinderZ (const T _length, const T _radius, const Quaternion< T > &_rot)
	Set inertial properties based on equivalent cylinder aligned with Z axis using the current mass value. More...

bool	SetFromCylinderZ (const T _mass, const T _length, const T _radius, const Quaternion< T > &_rot=Quaternion< T >::Identity)
	Set inertial properties based on mass and equivalent cylinder aligned with Z axis. More...

bool	SetFromSphere (const Material &_mat, const T _radius)
	Set inertial properties based on a material and equivalent sphere. More...

bool	SetFromSphere (const T _mass, const T _radius)
	Set inertial properties based on mass and equivalent sphere. More...

bool	SetFromSphere (const T _radius)
	Set inertial properties based on equivalent sphere using the current mass value. More...

bool	SetInertiaMatrix (const T &_ixx, const T &_iyy, const T &_izz, const T &_ixy, const T &_ixz, const T &_iyz)
	Set the moment of inertia matrix. More...

bool	SetIxx (const T &_v)
	Set IXX. More...

bool	SetIxy (const T &_v)
	Set IXY. More...

bool	SetIxz (const T &_v)
	Set IXZ. More...

bool	SetIyy (const T &_v)
	Set IYY. More...

bool	SetIyz (const T &_v)
	Set IYZ. More...

bool	SetIzz (const T &_v)
	Set IZZ. More...

bool	SetMass (const T &_m)
	Set the mass. More...

bool	SetMoi (const Matrix3< T > &_moi)
	Sets Moments of Inertia (MOI) from a Matrix3. Symmetric component of input matrix is used by averaging off-axis terms. More...

bool	SetOffDiagonalMoments (const Vector3< T > &_ixyxzyz)
	Set the off-diagonal moments of inertia (Ixy, Ixz, Iyz). More...

Static Public Member Functions
static T	Epsilon (const Vector3< T > &_moments, const T _tolerance=GZ_MASSMATRIX3_DEFAULT_TOLERANCE< T >)
	Get an epsilon value that represents the amount of acceptable error in a MassMatrix3. The epsilon value is related to machine precision multiplied by the largest possible moment of inertia. More...

static bool	ValidMoments (const Vector3< T > &_moments, const T _tolerance=GZ_MASSMATRIX3_DEFAULT_TOLERANCE< T >)
	Verify that principal moments are positive and satisfy the triangle inequality. More...

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Detailed Description

template<typename T>
class gz::math::MassMatrix3< T >

A class for inertial information about a rigid body consisting of the scalar mass and a 3x3 symmetric moment of inertia matrix stored as two Vector3's.

Constructor & Destructor Documentation

◆ MassMatrix3() [1/3]

MassMatrix3 ( )

inline

Default Constructor, which inializes the mass and moments to zero.

◆ MassMatrix3() [2/3]

MassMatrix3	(	const T &	_mass,
		const Vector3< T > &	_ixxyyzz,
		const Vector3< T > &	_ixyxzyz
	)

inline

Constructor.

Parameters

[in]	_mass	Mass value in kg if using metric.
[in]	_ixxyyzz	Diagonal moments of inertia.
[in]	_ixyxzyz	Off-diagonal moments of inertia

◆ MassMatrix3() [3/3]

MassMatrix3 ( const MassMatrix3< T > & _m )

default

Copy constructor.

Parameters

[in] _m MassMatrix3 element to copy

◆ ~MassMatrix3()

~MassMatrix3 ( )

default

Destructor.

Member Function Documentation

◆ DiagonalMoments()

Vector3<T> DiagonalMoments ( ) const

inline

Get the diagonal moments of inertia (Ixx, Iyy, Izz).

Returns: The diagonal moments.

Referenced by MassMatrix3< T >::Epsilon(), and MassMatrix3< T >::operator==().

◆ Epsilon() [1/2]

T Epsilon ( const T _tolerance = GZ_MASSMATRIX3_DEFAULT_TOLERANCE<T> ) const

inline

Get an epsilon value that represents the amount of acceptable error in a MassMatrix3. The epsilon value is related to machine precision multiplied by the largest possible moment of inertia.

Parameters

[in] _tolerance A factor that is used to adjust the return value. A value of zero will cause the return value to be zero. A good value is 10, which is also the MASSMATRIX3_DEFAULT_TOLERANCE.

References MassMatrix3< T >::DiagonalMoments().

Referenced by MassMatrix3< T >::IsNearPositive(), MassMatrix3< T >::IsPositive(), and MassMatrix3< T >::ValidMoments().

◆ Epsilon() [2/2]

static T Epsilon	(	const Vector3< T > &	_moments,
		const T	_tolerance = `GZ_MASSMATRIX3_DEFAULT_TOLERANCE<T>`
	)

inlinestatic

Get an epsilon value that represents the amount of acceptable error in a MassMatrix3. The epsilon value is related to machine precision multiplied by the largest possible moment of inertia.

This function is used by IsValid(), IsNearPositive(), IsPositive(), and ValidMoments().

Parameters

[in]	_moments	Principal moments of inertia.
[in]	_tolerance	A factor that is used to adjust the return value. A value of zero will cause the return value to be zero. A good value is 10, which is also the MASSMATRIX3_DEFAULT_TOLERANCE.

Returns: The epsilon value computed using:

T maxPossibleMoI = 0.5 * std::abs(_moments.Sum());
return _tolerance *
  std::numeric_limits<T>::epsilon() * maxPossibleMoI;

References numeric_limits::epsilon(), and Vector3< T >::Sum().

◆ EquivalentBox()

bool EquivalentBox	(	Vector3< T > &	_size,
		Quaternion< T > &	_rot,
		const T	_tol = `1e-6`
	)		const

inline

Get dimensions and rotation offset of uniform box with equivalent mass and moment of inertia. To compute this, the Matrix3 is diagonalized. The eigenvalues on the diagonal and the rotation offset of the principal axes are returned.

Parameters

[in]	_size	Dimensions of box aligned with principal axes.
[in]	_rot	Rotational offset of principal axes.
[in]	_tol	Relative tolerance.

Returns: True if box properties were computed successfully.

Todo:: Use a mock class to test this line

References MassMatrix3< T >::IsPositive(), MassMatrix3< T >::PrincipalAxesOffset(), MassMatrix3< T >::PrincipalMoments(), MassMatrix3< T >::ValidMoments(), Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ IsNearPositive()

bool IsNearPositive ( const T _tolerance = GZ_MASSMATRIX3_DEFAULT_TOLERANCE<T> ) const

inline

Verify that inertia values are positive semidefinite.

Parameters

[in] _tolerance The amount of relative error to accept when checking whether this MassMatrix3 has a valid mass and moment of inertia. Refer to Epsilon() for a description of _tolerance.

Returns: True if mass is nonnegative and moment of inertia matrix is positive semidefinite. The following is how the return value is calculated

const T epsilon = this->Epsilon(_tolerance);
return (this->mass + epsilon >= 0) &&
        (this->IXX() + epsilon  >= 0) &&
        (this->IXX() * this->IYY() - std::pow(this->IXY(), 2) +
         epsilon >= 0) &&
        (this->Moi().Determinant() + epsilon >= 0);

References MassMatrix3< T >::Epsilon(), MassMatrix3< T >::Ixx(), MassMatrix3< T >::Ixy(), MassMatrix3< T >::Iyy(), MassMatrix3< T >::Moi(), and std::pow().

Referenced by MassMatrix3< T >::IsValid().

◆ IsPositive()

bool IsPositive ( const T _tolerance = GZ_MASSMATRIX3_DEFAULT_TOLERANCE<T> ) const

inline

Verify that inertia values are positive definite.

Parameters

[in] _tolerance The amount of error to accept when checking whether this MassMatrix3 has a valid mass and moment of inertia. Refer to Epsilon() for a description of _tolerance.

Returns: True if mass is positive and moment of inertia matrix is positive definite. The following is how the return value is calculated

const T epsilon = this->Epsilon(_tolerance);
return (this->mass + epsilon > 0) &&
        (this->IXX() + epsilon  > 0) &&
        (this->IXX() * this->IYY() - std::pow(this->IXY(), 2) +
         epsilon > 0) &&
        (this->Moi().Determinant() + epsilon > 0);

References MassMatrix3< T >::Epsilon(), MassMatrix3< T >::Ixx(), MassMatrix3< T >::Ixy(), MassMatrix3< T >::Iyy(), MassMatrix3< T >::Moi(), and std::pow().

Referenced by MassMatrix3< T >::EquivalentBox().

◆ IsValid()

bool IsValid ( const T _tolerance = GZ_MASSMATRIX3_DEFAULT_TOLERANCE<T> ) const

inline

Verify that inertia values are positive semi-definite and satisfy the triangle inequality.

Parameters

[in] _tolerance The amount of error to accept when checking whether the MassMatrix3 has a valid mass and moment of inertia. This value is passed on to IsNearPositive() and ValidMoments(), which in turn pass the tolerance value to Epsilon(). Refer to Epsilon() for a description of _tolerance.

Returns: True if IsNearPositive(_tolerance) and ValidMoments(this->PrincipalMoments(), _tolerance) both return true.

References MassMatrix3< T >::IsNearPositive(), MassMatrix3< T >::PrincipalMoments(), and MassMatrix3< T >::ValidMoments().

Referenced by MassMatrix3< T >::SetDiagonalMoments(), MassMatrix3< T >::SetInertiaMatrix(), MassMatrix3< T >::SetIxx(), MassMatrix3< T >::SetIxy(), MassMatrix3< T >::SetIxz(), MassMatrix3< T >::SetIyy(), MassMatrix3< T >::SetIyz(), MassMatrix3< T >::SetIzz(), MassMatrix3< T >::SetMass(), MassMatrix3< T >::SetMoi(), and MassMatrix3< T >::SetOffDiagonalMoments().

◆ Ixx()

T Ixx ( ) const

inline

Get IXX.

Returns: IXX value

Referenced by MassMatrix3< T >::IsNearPositive(), and MassMatrix3< T >::IsPositive().

◆ Ixy()

T Ixy ( ) const

inline

Get IXY.

Returns: IXY value

Referenced by MassMatrix3< T >::IsNearPositive(), and MassMatrix3< T >::IsPositive().

◆ Ixz()

T Ixz ( ) const

inline

Get IXZ.

Returns: IXZ value

◆ Iyy()

T Iyy ( ) const

inline

Get IYY.

Returns: IYY value

Referenced by MassMatrix3< T >::IsNearPositive(), and MassMatrix3< T >::IsPositive().

◆ Iyz()

T Iyz ( ) const

inline

Get IYZ.

Returns: IYZ value

◆ Izz()

T Izz ( ) const

inline

Get IZZ.

Returns: IZZ value

◆ Mass()

T Mass ( ) const

inline

Get the mass.

Returns: The mass value

Referenced by MassMatrix3< T >::operator==(), MassMatrix3< T >::SetFromBox(), MassMatrix3< T >::SetFromConeZ(), MassMatrix3< T >::SetFromCylinderZ(), and MassMatrix3< T >::SetFromSphere().

◆ Moi()

Matrix3<T> Moi ( ) const

inline

returns Moments of Inertia as a Matrix3

Returns: Moments of Inertia as a Matrix3

Referenced by MassMatrix3< T >::IsNearPositive(), and MassMatrix3< T >::IsPositive().

◆ OffDiagonalMoments()

Vector3<T> OffDiagonalMoments ( ) const

inline

Get the off-diagonal moments of inertia (Ixy, Ixz, Iyz).

Returns: The off-diagonal moments of inertia.

Referenced by MassMatrix3< T >::operator==().

◆ operator!=()

bool operator!= ( const MassMatrix3< T > & _m ) const

inline

Inequality test operator.

Parameters

[in] _m MassMatrix3<T> to test

Returns: True if not equal (using the default tolerance of 1e-6)

◆ operator=()

MassMatrix3& operator= ( const MassMatrix3< T > & _massMatrix )

default

Equal operator.

Parameters

[in] _massMatrix MassMatrix3 to copy.

Returns: Reference to this object.

◆ operator==()

bool operator== ( const MassMatrix3< T > & _m ) const

inline

Equality comparison operator.

Parameters

[in] _m MassMatrix3 to copy.

Returns: true if each component is equal within a default tolerance, false otherwise

References MassMatrix3< T >::DiagonalMoments(), MassMatrix3< T >::Mass(), and MassMatrix3< T >::OffDiagonalMoments().

◆ PrincipalAxesOffset()

Quaternion<T> PrincipalAxesOffset ( const T _tol = 1e-6 ) const

inline

Compute rotational offset of principal axes.

Parameters

[in] _tol Relative tolerance given by absolute value of _tol. Negative values of _tol are interpreted as a flag that causes principal moments to always be sorted from smallest to largest.

Returns: Quaternion representing rotational offset of principal axes. With a rotation matrix constructed from this quaternion R(q) and a diagonal matrix L with principal moments on the diagonal, the original moment of inertia matrix MOI can be reconstructed with MOI = R(q).Transpose() * L * R(q)

Todo:: Use a mock class to test this line

References Vector3< T >::Equal(), GZ_PI_2, Quaternion< T >::Inverse(), Angle::Normalize(), std::pow(), MassMatrix3< T >::PrincipalMoments(), Angle::Radian(), Vector2< T >::Set(), and Vector2< T >::SquaredLength().

Referenced by MassMatrix3< T >::EquivalentBox().

◆ PrincipalMoments()

Vector3<T> PrincipalMoments ( const T _tol = 1e-6 ) const

inline

Compute principal moments of inertia, which are the eigenvalues of the moment of inertia matrix.

Parameters

[in] _tol Relative tolerance given by absolute value of _tol. Negative values of _tol are interpreted as a flag that causes principal moments to always be sorted from smallest to largest.

Returns: Principal moments of inertia. If the matrix is already diagonal and _tol is positive, they are returned in the existing order. Otherwise, the moments are sorted from smallest to largest.

References GZ_PI, std::pow(), gz::math::sort3(), and Vector3< T >::Sum().

Referenced by MassMatrix3< T >::EquivalentBox(), MassMatrix3< T >::IsValid(), and MassMatrix3< T >::PrincipalAxesOffset().

◆ SetDiagonalMoments()

bool SetDiagonalMoments ( const Vector3< T > & _ixxyyzz )

inline

Set the diagonal moments of inertia (Ixx, Iyy, Izz).

Parameters

[in] _ixxyyzz diagonal moments of inertia

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetFromBox() [1/3]

bool SetFromBox	(	const Material &	_mat,
		const Vector3< T > &	_size,
		const Quaternion< T > &	_rot = `Quaternion<T>::Identity`
	)

inline

Set inertial properties based on a Material and equivalent box.

Parameters

[in]	_mat	Material that specifies a density. Uniform density is used.
[in]	_size	Size of equivalent box.
[in]	_rot	Rotational offset of equivalent box.

Returns: True if inertial properties were set successfully.

References Material::Density(), Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

Referenced by OrientedBox< T >::MassMatrix(), and MassMatrix3< T >::SetFromBox().

◆ SetFromBox() [2/3]

bool SetFromBox	(	const T	_mass,
		const Vector3< T > &	_size,
		const Quaternion< T > &	_rot = `Quaternion<T>::Identity`
	)

inline

Set inertial properties based on mass and equivalent box.

Parameters

[in]	_mass	Mass to set.
[in]	_size	Size of equivalent box.
[in]	_rot	Rotational offset of equivalent box.

Returns: True if inertial properties were set successfully.

References Vector3< T >::Min(), MassMatrix3< T >::SetFromBox(), and MassMatrix3< T >::SetMass().

◆ SetFromBox() [3/3]

bool SetFromBox	(	const Vector3< T > &	_size,
		const Quaternion< T > &	_rot = `Quaternion<T>::Identity`
	)

inline

Set inertial properties based on equivalent box using the current mass value.

Parameters

[in]	_size	Size of equivalent box.
[in]	_rot	Rotational offset of equivalent box.

Returns: True if inertial properties were set successfully.

References MassMatrix3< T >::Mass(), Vector3< T >::Min(), std::pow(), MassMatrix3< T >::SetMoi(), Matrix3< T >::Transposed(), Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ SetFromConeZ() [1/3]

bool SetFromConeZ	(	const Material &	_mat,
		const T	_length,
		const T	_radius,
		const Quaternion< T > &	_rot = `Quaternion<T>::Identity`
	)

inline

Set inertial properties based on a Material and equivalent cone aligned with Z axis.

Parameters

[in]	_mat	Material that specifies a density. Uniform density is used.
[in]	_length	Length of cone along Z axis.
[in]	_radius	Radius of cone.
[in]	_rot	Rotational offset of equivalent cone.

Returns: True if inertial properties were set successfully.

References Material::Density(), and GZ_PI.

Referenced by MassMatrix3< T >::SetFromConeZ().

◆ SetFromConeZ() [2/3]

bool SetFromConeZ	(	const T	_length,
		const T	_radius,
		const Quaternion< T > &	_rot
	)

inline

Set inertial properties based on equivalent cone aligned with Z axis using the current mass value.

Parameters

[in]	_length	Length of cone along Z axis.
[in]	_radius	Radius of cone.
[in]	_rot	Rotational offset of equivalent cone.

Returns: True if inertial properties were set successfully.

References MassMatrix3< T >::Mass(), std::pow(), MassMatrix3< T >::SetMoi(), and Matrix3< T >::Transposed().

◆ SetFromConeZ() [3/3]

bool SetFromConeZ	(	const T	_mass,
		const T	_length,
		const T	_radius,
		const Quaternion< T > &	_rot = `Quaternion<T>::Identity`
	)

inline

Set inertial properties based on mass and equivalent cone aligned with Z axis.

Parameters

[in]	_mass	Mass to set.
[in]	_length	Length of cone along Z axis.
[in]	_radius	Radius of cone.
[in]	_rot	Rotational offset of equivalent cone.

Returns: True if inertial properties were set successfully.

References MassMatrix3< T >::SetFromConeZ(), and MassMatrix3< T >::SetMass().

◆ SetFromCylinderZ() [1/3]

bool SetFromCylinderZ	(	const Material &	_mat,
		const T	_length,
		const T	_radius,
		const Quaternion< T > &	_rot = `Quaternion<T>::Identity`
	)

inline

Set inertial properties based on a Material and equivalent cylinder aligned with Z axis.

Parameters

[in]	_mat	Material that specifies a density. Uniform density is used.
[in]	_length	Length of cylinder along Z axis.
[in]	_radius	Radius of cylinder.
[in]	_rot	Rotational offset of equivalent cylinder.

Returns: True if inertial properties were set successfully.

References Material::Density(), and GZ_PI.

Referenced by MassMatrix3< T >::SetFromCylinderZ().

◆ SetFromCylinderZ() [2/3]

bool SetFromCylinderZ	(	const T	_length,
		const T	_radius,
		const Quaternion< T > &	_rot
	)

inline

Set inertial properties based on equivalent cylinder aligned with Z axis using the current mass value.

Parameters

[in]	_length	Length of cylinder along Z axis.
[in]	_radius	Radius of cylinder.
[in]	_rot	Rotational offset of equivalent cylinder.

Returns: True if inertial properties were set successfully.

References MassMatrix3< T >::Mass(), std::pow(), MassMatrix3< T >::SetMoi(), and Matrix3< T >::Transposed().

◆ SetFromCylinderZ() [3/3]

bool SetFromCylinderZ	(	const T	_mass,
		const T	_length,
		const T	_radius,
		const Quaternion< T > &	_rot = `Quaternion<T>::Identity`
	)

inline

Set inertial properties based on mass and equivalent cylinder aligned with Z axis.

Parameters

[in]	_mass	Mass to set.
[in]	_length	Length of cylinder along Z axis.
[in]	_radius	Radius of cylinder.
[in]	_rot	Rotational offset of equivalent cylinder.

Returns: True if inertial properties were set successfully.

References MassMatrix3< T >::SetFromCylinderZ(), and MassMatrix3< T >::SetMass().

◆ SetFromSphere() [1/3]

bool SetFromSphere	(	const Material &	_mat,
		const T	_radius
	)

inline

Set inertial properties based on a material and equivalent sphere.

Parameters

[in]	_mat	Material that specifies a density. Uniform density is used.
[in]	_radius	Radius of equivalent, uniform sphere.

Returns: True if inertial properties were set successfully.

References Material::Density(), GZ_PI, and std::pow().

Referenced by MassMatrix3< T >::SetFromSphere().

◆ SetFromSphere() [2/3]

bool SetFromSphere	(	const T	_mass,
		const T	_radius
	)

inline

Set inertial properties based on mass and equivalent sphere.

Parameters

[in]	_mass	Mass to set.
[in]	_radius	Radius of equivalent, uniform sphere.

Returns: True if inertial properties were set successfully.

References MassMatrix3< T >::SetFromSphere(), and MassMatrix3< T >::SetMass().

◆ SetFromSphere() [3/3]

bool SetFromSphere ( const T _radius )

inline

Set inertial properties based on equivalent sphere using the current mass value.

Parameters

[in] _radius Radius of equivalent, uniform sphere.

Returns: True if inertial properties were set successfully.

References MassMatrix3< T >::Mass(), std::pow(), and MassMatrix3< T >::SetMoi().

◆ SetInertiaMatrix()

bool SetInertiaMatrix	(	const T &	_ixx,
		const T &	_iyy,
		const T &	_izz,
		const T &	_ixy,
		const T &	_ixz,
		const T &	_iyz
	)

inline

Set the moment of inertia matrix.

Parameters

[in]	_ixx	X second moment of inertia (MOI) about x axis.
[in]	_iyy	Y second moment of inertia about y axis.
[in]	_izz	Z second moment of inertia about z axis.
[in]	_ixy	XY inertia.
[in]	_ixz	XZ inertia.
[in]	_iyz	YZ inertia.

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetIxx()

bool SetIxx ( const T & _v )

inline

Set IXX.

Parameters

[in] _v IXX value

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetIxy()

bool SetIxy ( const T & _v )

inline

Set IXY.

Parameters

[in] _v IXY value

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetIxz()

bool SetIxz ( const T & _v )

inline

Set IXZ.

Parameters

[in] _v IXZ value

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetIyy()

bool SetIyy ( const T & _v )

inline

Set IYY.

Parameters

[in] _v IYY value

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetIyz()

bool SetIyz ( const T & _v )

inline

Set IYZ.

Parameters

[in] _v IYZ value

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetIzz()

bool SetIzz ( const T & _v )

inline

Set IZZ.

Parameters

[in] _v IZZ value

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ SetMass()

bool SetMass ( const T & _m )

inline

Set the mass.

Parameters

[in] _m New mass value.

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

Referenced by MassMatrix3< T >::SetFromBox(), MassMatrix3< T >::SetFromConeZ(), MassMatrix3< T >::SetFromCylinderZ(), and MassMatrix3< T >::SetFromSphere().

◆ SetMoi()

bool SetMoi ( const Matrix3< T > & _moi )

inline

Sets Moments of Inertia (MOI) from a Matrix3. Symmetric component of input matrix is used by averaging off-axis terms.

Parameters

[in] _moi Moments of Inertia as a Matrix3

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

Referenced by MassMatrix3< T >::SetFromBox(), MassMatrix3< T >::SetFromConeZ(), MassMatrix3< T >::SetFromCylinderZ(), and MassMatrix3< T >::SetFromSphere().

◆ SetOffDiagonalMoments()

bool SetOffDiagonalMoments ( const Vector3< T > & _ixyxzyz )

inline

Set the off-diagonal moments of inertia (Ixy, Ixz, Iyz).

Parameters

[in] _ixyxzyz off-diagonal moments of inertia

Returns: True if the MassMatrix3 is valid.

References MassMatrix3< T >::IsValid().

◆ ValidMoments()

static bool ValidMoments	(	const Vector3< T > &	_moments,
		const T	_tolerance = `GZ_MASSMATRIX3_DEFAULT_TOLERANCE<T>`
	)

inlinestatic

Verify that principal moments are positive and satisfy the triangle inequality.

Parameters

[in]	_moments	Principal moments of inertia.
[in]	_tolerance	The amount of error to accept when checking whether the moments are positive and satisfy the triangle inequality. Refer to Epsilon() for a description of _tolerance.

Returns: True if moments of inertia are positive and satisfy the triangle inequality. The following is how the return value is calculated.

T epsilon = this->Epsilon(_tolerance);
 
return _moments[0] + epsilon >= 0 &&
  _moments[1] + epsilon >= 0 &&
  _moments[2] + epsilon >= 0 &&
  _moments[0] + _moments[1] + epsilon >= _moments[2] &&
  _moments[1] + _moments[2] + epsilon >= _moments[0] &&
  _moments[2] + _moments[0] + epsilon >= _moments[1];

References MassMatrix3< T >::Epsilon().

Referenced by MassMatrix3< T >::EquivalentBox(), and MassMatrix3< T >::IsValid().

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

gz/math/MassMatrix3.hh

Public Member Functions

Static Public Member Functions

Detailed Description

template<typename T> class gz::math::MassMatrix3< T >

Constructor & Destructor Documentation

◆ MassMatrix3() [1/3]

◆ MassMatrix3() [2/3]

◆ MassMatrix3() [3/3]

◆ ~MassMatrix3()

Member Function Documentation

◆ DiagonalMoments()

◆ Epsilon() [1/2]

◆ Epsilon() [2/2]

◆ EquivalentBox()

◆ IsNearPositive()

◆ IsPositive()

◆ IsValid()

◆ Ixx()

◆ Ixy()

◆ Ixz()

◆ Iyy()

◆ Iyz()

◆ Izz()

◆ Mass()

◆ Moi()

◆ OffDiagonalMoments()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ PrincipalAxesOffset()

◆ PrincipalMoments()

◆ SetDiagonalMoments()

◆ SetFromBox() [1/3]

◆ SetFromBox() [2/3]

◆ SetFromBox() [3/3]

◆ SetFromConeZ() [1/3]

◆ SetFromConeZ() [2/3]

◆ SetFromConeZ() [3/3]

◆ SetFromCylinderZ() [1/3]

◆ SetFromCylinderZ() [2/3]

◆ SetFromCylinderZ() [3/3]

◆ SetFromSphere() [1/3]

◆ SetFromSphere() [2/3]

◆ SetFromSphere() [3/3]

◆ SetInertiaMatrix()

◆ SetIxx()

◆ SetIxy()

◆ SetIxz()

◆ SetIyy()

◆ SetIyz()

◆ SetIzz()

◆ SetMass()

◆ SetMoi()

◆ SetOffDiagonalMoments()

◆ ValidMoments()

template<typename T>
class gz::math::MassMatrix3< T >