#include <MassProperties.hpp>

Public Member Functions
Mat3< Scalar >	inertia_about_point (const Vec3< Scalar > &point) const
MassProperties< Scalar >	operator+ (const MassProperties< Scalar > &other) const
MassProperties< Scalar >	operator- (const MassProperties< Scalar > &other) const
MassProperties< Scalar >	operator* (const Scalar &factor) const
MassProperties< Scalar >	operator/ (const Scalar &factor) const
	Divide mass properties by a factor.
MassProperties< Scalar > &	operator+= (const MassProperties< Scalar > &other)
	In-place addition.
Vec3< Scalar >	cg_offset () const

Static Public Member Functions
static MassProperties< Scalar >	point_mass (const Scalar &m, const Vec3< Scalar > &position)
static MassProperties< Scalar >	diagonal (const Scalar &m, const Vec3< Scalar > &cg_pos, const Scalar &Ixx, const Scalar &Iyy, const Scalar &Izz)
static MassProperties< Scalar >	from_components (const Scalar &m, const Vec3< Scalar > &cg_pos, const Scalar &Ixx, const Scalar &Iyy, const Scalar &Izz, const Scalar &Ixy, const Scalar &Ixz, const Scalar &Iyz)
static MassProperties< Scalar >	solid_sphere (const Scalar &m, const Scalar &radius, const Vec3< Scalar > &cg_pos=Vec3< Scalar >::Zero())
static MassProperties< Scalar >	solid_cylinder (const Scalar &m, const Scalar &radius, const Scalar &length, const Vec3< Scalar > &cg_pos=Vec3< Scalar >::Zero())
static MassProperties< Scalar >	solid_box (const Scalar &m, const Scalar &dx, const Scalar &dy, const Scalar &dz, const Vec3< Scalar > &cg_pos=Vec3< Scalar >::Zero())
static MassProperties< Scalar >	from_mass (const Scalar &m)
static MassProperties< Scalar >	diagonal (const Scalar &m, const Scalar &Ixx, const Scalar &Iyy, const Scalar &Izz)
static MassProperties< Scalar >	full (const Scalar &m, const Scalar &Ixx, const Scalar &Iyy, const Scalar &Izz, const Scalar &Ixy, const Scalar &Ixz, const Scalar &Iyz)

Public Attributes
Scalar	mass
	Total mass [kg].
Vec3< Scalar >	cg
	CG position in body frame [m].
Mat3< Scalar >	inertia
	Inertia tensor about CG, in body-fixed axes [kg·m²].

Detailed Description

template<typename Scalar>
struct vulcan::mass::MassProperties< Scalar >

Full mass properties for a rigid body component

All quantities are expressed in body-fixed coordinates:

cg: Position of the center of gravity in the body frame, measured from the body frame origin (typically a reference point like nose, or structural origin) [m]
inertia: Inertia tensor about the CG, expressed in body-fixed axes (i.e., the tensor components Ixx, Ixy, etc. are with respect to body X, Y, Z axes) [kg·m²]

Frame Convention

Body Frame (typical aerospace convention):
  - X: Forward (out the nose)
  - Y: Right (starboard wing)
  - Z: Down
 
CG position is a 3-vector [x_cg, y_cg, z_cg] in body coordinates.
Inertia tensor is 3x3, about CG, with components in body axes.

When passed to dynamics functions like compute_6dof_derivatives(), the mass properties must be consistent with the body frame used for forces, moments, and angular velocity.

Inertia Tensor Convention

Uses the STANDARD mathematical convention:

| Ixx  Ixy  Ixz |
| Ixy  Iyy  Iyz |
| Ixz  Iyz  Izz |

where Ixy = -∫xy dm (negative product of inertia).

This differs from some CAD tools (SolidWorks, NX) which use opposite signs.

Reference: https://en.wikipedia.org/wiki/Moment_of_inertia#Inertia_tensor

Aggregation

Mass properties can be combined using operator+:

auto total = wing + fuselage + tail;

The combined CG is the mass-weighted average, and inertia is computed using the parallel axis theorem. All components must be expressed in the same body frame for aggregation to be meaningful.

Member Function Documentation

◆ cg_offset()

template<typename Scalar>

Vec3< Scalar > vulcan::mass::MassProperties< Scalar >::cg_offset ( ) const

inline

Get CG offset from origin (alias for cg)

Deprecated: Use cg directly

◆ diagonal() [1/2]

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::diagonal	(	const Scalar &	m,
		const Scalar &	Ixx,
		const Scalar &	Iyy,
		const Scalar &	Izz )

inlinestatic

Create with diagonal inertia at origin (4-arg overload)

Deprecated: Use diagonal(m, cg, Ixx, Iyy, Izz) instead

◆ diagonal() [2/2]

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::diagonal	(	const Scalar &	m,
		const Vec3< Scalar > &	cg_pos,
		const Scalar &	Ixx,
		const Scalar &	Iyy,
		const Scalar &	Izz )

inlinestatic

Create mass properties with diagonal inertia tensor

Parameters

m	Mass [kg]
cg_pos	CG position [m]
Ixx	Principal moment about X [kg·m²]
Iyy	Principal moment about Y [kg·m²]
Izz	Principal moment about Z [kg·m²]

◆ from_components()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::from_components	(	const Scalar &	m,
		const Vec3< Scalar > &	cg_pos,
		const Scalar &	Ixx,
		const Scalar &	Iyy,
		const Scalar &	Izz,
		const Scalar &	Ixy,
		const Scalar &	Ixz,
		const Scalar &	Iyz )

inlinestatic

Create mass properties with full 6-component inertia tensor

Products of inertia use POSITIVE convention: Ixy_input = ∫xy dm The function applies negation internally to form the standard tensor.

Parameters

m	Mass [kg]
cg_pos	CG position [m]
Ixx	Moment about X [kg·m²]
Iyy	Moment about Y [kg·m²]
Izz	Moment about Z [kg·m²]
Ixy	Product of inertia (positive convention) [kg·m²]
Ixz	Product of inertia (positive convention) [kg·m²]
Iyz	Product of inertia (positive convention) [kg·m²]

◆ from_mass()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::from_mass ( const Scalar & m )

inlinestatic

Create from mass only (point mass at origin)

Deprecated: Use point_mass() instead

◆ full()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::full	(	const Scalar &	m,
		const Scalar &	Ixx,
		const Scalar &	Iyy,
		const Scalar &	Izz,
		const Scalar &	Ixy,
		const Scalar &	Ixz,
		const Scalar &	Iyz )

inlinestatic

Create with full inertia at origin (7-arg overload)

Deprecated: Use from_components() instead

◆ inertia_about_point()

template<typename Scalar>

Mat3< Scalar > vulcan::mass::MassProperties< Scalar >::inertia_about_point ( const Vec3< Scalar > & point ) const

inline

Get inertia tensor about an arbitrary point

Uses the parallel axis theorem (tensor generalization): J = I + m * (|r|² * Identity - r ⊗ r)

where r is the vector from the point to the CG.

Reference: https://en.wikipedia.org/wiki/Parallel_axis_theorem#Tensor_generalization

Parameters

point The reference point [m]

Returns: Inertia tensor about that point [kg·m²]

◆ operator*()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::operator* ( const Scalar & factor ) const

inline

Scale mass properties by a factor

Scales mass and inertia; CG remains unchanged.

◆ operator+()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::operator+ ( const MassProperties< Scalar > & other ) const

inline

Add two mass properties (aggregation)

Computes combined CG as mass-weighted average, then uses parallel axis theorem to express both inertias about the combined CG and sums them.

◆ operator+=()

template<typename Scalar>

MassProperties< Scalar > & vulcan::mass::MassProperties< Scalar >::operator+= ( const MassProperties< Scalar > & other )

inline

In-place addition.

◆ operator-()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::operator- ( const MassProperties< Scalar > & other ) const

inline

Subtract mass properties (hole removal)

Used for modeling holes or removed material.

◆ operator/()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::operator/ ( const Scalar & factor ) const

inline

Divide mass properties by a factor.

◆ point_mass()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::point_mass	(	const Scalar &	m,
		const Vec3< Scalar > &	position )

inlinestatic

Create a point mass at a specified location

A point mass has zero inertia about its own CG.

Parameters

m	Mass [kg]
position	CG position [m]

◆ solid_box()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::solid_box	(	const Scalar &	m,
		const Scalar &	dx,
		const Scalar &	dy,
		const Scalar &	dz,
		const Vec3< Scalar > &	cg_pos = Vec3<Scalar>::Zero() )

inlinestatic

Create mass properties for a solid rectangular box

Ixx = (1/12) * m * (dy² + dz²) Iyy = (1/12) * m * (dx² + dz²) Izz = (1/12) * m * (dx² + dy²)

Parameters

m	Mass [kg]
dx	Width in X [m]
dy	Width in Y [m]
dz	Width in Z [m]
cg_pos	CG position [m] (default: origin)

◆ solid_cylinder()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::solid_cylinder	(	const Scalar &	m,
		const Scalar &	radius,
		const Scalar &	length,
		const Vec3< Scalar > &	cg_pos = Vec3<Scalar>::Zero() )

inlinestatic

Create mass properties for a solid cylinder (axis along Z)

Ixx = Iyy = (1/12) * m * (3*r² + L²) Izz = (1/2) * m * r²

Parameters

m	Mass [kg]
radius	Cylinder radius [m]
length	Cylinder length along Z [m]
cg_pos	CG position [m] (default: origin)

◆ solid_sphere()

template<typename Scalar>

MassProperties< Scalar > vulcan::mass::MassProperties< Scalar >::solid_sphere	(	const Scalar &	m,
		const Scalar &	radius,
		const Vec3< Scalar > &	cg_pos = Vec3<Scalar>::Zero() )

inlinestatic

Create mass properties for a solid sphere

I = (2/5) * m * r² for all axes

Parameters

m	Mass [kg]
radius	Sphere radius [m]
cg_pos	CG position [m] (default: origin)

Member Data Documentation

◆ cg

template<typename Scalar>

Vec3<Scalar> vulcan::mass::MassProperties< Scalar >::cg

CG position in body frame [m].

◆ inertia

template<typename Scalar>

Mat3<Scalar> vulcan::mass::MassProperties< Scalar >::inertia

Inertia tensor about CG, in body-fixed axes [kg·m²].

◆ mass

template<typename Scalar>

Scalar vulcan::mass::MassProperties< Scalar >::mass

Total mass [kg].

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

include/vulcan/mass/MassProperties.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Frame Convention

Inertia Tensor Convention

Aggregation

Member Function Documentation

◆ cg_offset()

◆ diagonal() [1/2]

◆ diagonal() [2/2]

◆ from_components()

◆ from_mass()

◆ full()

◆ inertia_about_point()

◆ operator*()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator/()

◆ point_mass()

◆ solid_box()

◆ solid_cylinder()

◆ solid_sphere()

Member Data Documentation

◆ cg

◆ inertia

◆ mass