Rigid Body

Rigid body (link) mass properties and transforms. More...

Classes
struct	fsb::Inertia
	Inertia tensor. More...
struct	fsb::MassProps
	Mass properties of a body. More...
struct	fsb::PrincipalInertia
	Principal inertia of body. More...
struct	fsb::BodyCartesianPva
	Container of Cartesian pose, velocity, and acceleration for a list of bodies. More...
struct	fsb::Body
	Link body parameters. More...

Functions
Inertia	fsb::body_rotate_inertia (const Quaternion &rot, const Inertia &inertia)
	Rotate inertia tensor.
MassProps	fsb::body_transform_mass_props (const Transform &transf, const MassProps &mass_props)
	Transform mass properties.
Inertia	fsb::body_parallel_axis_inertia (real_t mass, const Vec3 &com, const Inertia &inertia)
	Apply parallel axis theorem to inertia tensor.
MassProps	fsb::body_combine (const MassProps &mass_props_a, const Transform &transf_ab, const MassProps &mass_props_b)
	Combine mass properties of two bodies in origin of common frame.
bool	fsb::body_inertia_principal_axis (const Inertia &inertia, PrincipalInertia &principal_inertia)
bool	fsb::body_validate_inertia_is_pd (const Inertia &inertia)
	Check if inertia tensor is positive definite.
Vec3	fsb::inertia_multiply_vector (const Inertia &inertia, const Vec3 &vec)
	Inertia tensor multiplication with vector.
Vec3	fsb::inertia_cross_multiply_vector (const Inertia &inertia, const Vec3 &vel)
	Cross product with inertia tensor and angular velocity.

Detailed Description

Rigid body (link) mass properties and transforms.

Function Documentation

body_combine()

MassProps fsb::body_combine	(	const MassProps &	mass_props_a,
		const Transform &	transf_ab,
		const MassProps &	mass_props_b
	)

Combine mass properties of two bodies in origin of common frame.

Inertia is with respect to center of mass

Parameters

[in]	mass_props_a	Mass properties of body A
[in]	transf_ab	Coordinate transform from body A to body B
[in]	mass_props_b	Mass properties of body B

Returns

Combined mass properties

body_inertia_principal_axis()

bool fsb::body_inertia_principal_axis	(	const Inertia &	inertia,
		PrincipalInertia &	principal_inertia
	)

Parameters

[in]	inertia
[out]	principal_inertia

Returns

true

false

body_parallel_axis_inertia()

Inertia fsb::body_parallel_axis_inertia	(	real_t	mass,
		const Vec3 &	com,
		const Inertia &	inertia
	)

Apply parallel axis theorem to inertia tensor.

The inertia tensor about the center of mass is translated to be about center of frame $0$ \( \mathcal{I}_0 = \mathcal{I} - m [\mathbf{p}_{0c}]^{\times} [\mathbf{p}_{0c}]^{\times} \)

Parameters

[in]	mass	Mass of body
[in]	com	Center of mass
[in]	inertia	Inertia tensor with respect to center of mass

Returns

Output inertia tensor with respect to origin

body_rotate_inertia()

Inertia fsb::body_rotate_inertia	(	const Quaternion &	rot,
		const Inertia &	inertia
	)

Rotate inertia tensor.

\( \mathbf{I}_0 = \mathbf{R}_{0a} \mathcal{I}_a \mathbf{R}^T_{0a} \)

Parameters

[in]	rot	Rotation quaternion
[in]	inertia	Inertia tensor

Returns

Rotated inertia tensor

body_transform_mass_props()

MassProps fsb::body_transform_mass_props	(	const Transform &	transf,
		const MassProps &	mass_props
	)

Transform mass properties.

The inertia tensor about the center of mass is rotated to the new frame \(0\) from \(a\):

\( \mathbf{I}_0 = \mathbf{R}_{0a} \mathcal{I}_a \mathbf{R}^T_{0a} \)

The center of mass is transformed as

\( \mathbf{p}_{0c} = \mathbf{R}_{0a} \mathbf{p}_{ac} + \mathbf{p}_{0a} \)

and the mass is constant.

Parameters

[in]	transf	Coordinate transform from old to new frame
[in]	mass_props	Mass properties

Returns

Mass properties in new coordinate frame

body_validate_inertia_is_pd()

bool fsb::body_validate_inertia_is_pd

(

const Inertia &

inertia

)

Check if inertia tensor is positive definite.

Parameters

inertia

Returns

true

false

inertia_cross_multiply_vector()

Vec3 fsb::inertia_cross_multiply_vector	(	const Inertia &	inertia,
		const Vec3 &	vel
	)

Cross product with inertia tensor and angular velocity.

\( \mathbf{v} = \left[ \omega \right]^{\times} \mathcal{I} \omega \)

Parameters

inertia	Inertia tensor
vel	Angular velocity vector

Returns

Result of cross product and multiplication

inertia_multiply_vector()

Vec3 fsb::inertia_multiply_vector	(	const Inertia &	inertia,
		const Vec3 &	vec
	)

Inertia tensor multiplication with vector.

\( \mathbf{v} = \mathcal{I} \mathbf{w} \)

Parameters

inertia	Inertia tensor
vec	Vector to multiply by inertia tensor

Returns

Result of multiplication