RigidBody Class Reference

Rigid body dynamics function, calculates derivative of a rigid body, given sum of moments and forces and the acting gravity field. More...

#include <RigidBody.hxx>

Public Member Functions
	RigidBody (double mass, double Jxx, double Jyy, double Jzz, double Jxy, double Jxz, double Jyz, int extrastates=0)
	Simple constructor for a rigid body dynamics module.
	~RigidBody ()
	Destructor.
void	initialize (double x, double y, double z, double u, double v, double w, double phi, double theta, double psi, double p, double q, double r)
	Initialize a state vector x.
void	derivative (VectorE &xd, double unused=0.0)
	Obtain and calculate the derivative, given sum of forces and moments and the gravitational field acting on the body.
template<class V >
void	derivative (V &xd, double unused=0.0)
	Obtain and calculate the derivative, given sum of forces and moments and the gravitational field acting on the body.
void	specific (Vector &sp)
	Calculate specific forces and moments, forces stored in elements 0, 1, and 2, moments in elements 3, 4 and 6.
void	zeroForces ()
	Initialize sum of forces on the body to zero.
void	applyBodyForce (const Vector3 &Fb, const Vector3 &point)
	Apply a force expressed in body coordinates.
void	applyInertialForce (const Vector &Fi, const Vector &point)
	Apply a force expressed in inertial coordinates, at a specific body point, give in body coordinates.
void	applyBodyMoment (const Vector &M)
	Apply a moment expressed in body coordinates.
void	changeState (const Vector &dx)
	Change the state vector by a quantity dx.
void	addInertialGravity (const Vector &g)
	Add a gravitational field; 3 element vector, gravitation expressed in the inertial system.
void	setState (const Vector &newx)
	Put in a new state vector.
void	changeMass (const double dm)
	Add to the mass of the body.
void	setMass (const double newm)
	Set a new mass.
void	output ()
	Calculate auxiliary outputs, V, \(\alpha\), \(\beta\), \(\phi\), \(\theta\) and \(\Psi\).
const Vector &	X () const
	Obtain the state, 13 elements.
const double	V () const
	Obtain speed.
const double	alpha () const
	Obtain alpha.
const double	beta () const
	Obtain beta.
const double	getMass () const
	Get current mass.
const double	phi () const
	Get euler angle phi.
const double	theta () const
	Get euler angle theta.
const double	psi () const
	Get euler angle psi.
const Matrix3 &	A ()
	Get the transformation matrix, for transforming a vector in earth coordinates to one in the body's coordinate system.

Protected Attributes
Vector	x
	State vector.

Detailed Description

Rigid body dynamics function, calculates derivative of a rigid body, given sum of moments and forces and the acting gravity field.

The contents of the state vector are:

u, v, w, x, y, z, p, q, r, l1, l2, l3, L

• u, v, w are the velocity of the body, in body coordinates.
• x, y, z are the position of the body, in inertial reference coordinates.
• p, q, r are the components of the rotational speed vector, in body coordinates
• l1, l2, l3, L are the elements of the quaternion describing the body attitude.

Note that the RigidBody class only calculates the derivatives. If you want to integrate the equations of motion, you need an integration routine. Two templated integration functions are available, integrate_euler() and integrate_rungekutta().

The normal procedure would be to create a class that derives from the RigidBody class. You can also indicate that a number of additional state variables is needed, the RigidBody class will make these available to you, from index 13 onward.

The normal "work cycle" would be to call RigidBody::zeroForces(), which zeroes forces and gravity applied to the body, then repeatedly call RigidBody::applyBodyForce(), RigidBody::applyInertialForce(), RigidBody::applyBodyMoment() RigidBody::addInertialGravity() as needed, until all forces (drag, lift, wheel forces, thrusters, whatever) and all gravitational effects have been applied.

Then call RigidBody::derivative() to obtain the derivative.

RigidBody::specific(), RigidBody::X() and RigidBody::phi(), RigidBody::theta(), RigidBody::psi() can be used to get your outputs.

Examples

PulsedBody.cxx.

Constructor & Destructor Documentation

RigidBody()

RigidBody::RigidBody	(	double	mass,
		double	Jxx,
		double	Jyy,
		double	Jzz,
		double	Jxy,
		double	Jxz,
		double	Jyz,
		int	extrastates = 0 )

Simple constructor for a rigid body dynamics module.

Note that motion is always described around center of mass.

Parameters

mass	mass of the object
Jxx	Moment of inertia around x axis
Jyy	Moment of inertia around y axis
Jzz	Moment of inertia around z axis
Jxy	Inertia cross product x and y
Jxz	Inertia cross product x and z
Jyz	Inertia cross product y and z
extrastates	Number of additional states needed by derived classes.

Member Function Documentation

initialize()

void RigidBody::initialize	(	double	x,
		double	y,
		double	z,
		double	u,
		double	v,
		double	w,
		double	phi,
		double	theta,
		double	psi,
		double	p,
		double	q,
		double	r )

Initialize a state vector x.

Remember that x has 13 elements, due to the use of a quaternion representation.

Parameters

x	Carthesian position, x direction
y	Carthesian position, y direction
z	Carthesian position, z direction
u	Velocity, along body x axis
v	Velocity, along body y axis
w	Velocity, along body z axis
phi	Euler angle phi
theta	Euler angle theta
psi	Euler angle psi
p	Rotational velocity, along body x axis
q	Rotational velocity, along body y axis
r	Rotational velocity, along body z axis

derivative() [1/2]

void RigidBody::derivative	(	VectorE &	xd,
		double	unused = 0.0 )

Obtain and calculate the derivative, given sum of forces and moments and the gravitational field acting on the body.

Parameters

xd	Resultant derivative vector
unused	Unused variable, for compatibility with integration functions.

Examples

PulsedBody.cxx.

derivative() [2/2]

template<class V >

void RigidBody::derivative ( V & xd, double unused = 0.0 )

inline

Obtain and calculate the derivative, given sum of forces and moments and the gravitational field acting on the body.

Template Parameters

V	Vector type

Parameters

xd	Resultant derivative vector
unused	Unused variable, for compatibility with integration functions.

specific()

void RigidBody::specific

(

Vector &

sp

)

Calculate specific forces and moments, forces stored in elements 0, 1, and 2, moments in elements 3, 4 and 6.

Forces and moments calculated in body coordinates.

Parameters

sp	Vector with 6 elements, for result.

zeroForces()

void RigidBody::zeroForces

(

)

Initialize sum of forces on the body to zero.

Call before applying a new set of forces and moments.

applyBodyForce()

void RigidBody::applyBodyForce	(	const Vector3 &	Fb,
		const Vector3 &	point )

Apply a force expressed in body coordinates.

at a specific body point.

setState()

void RigidBody::setState

(

const Vector &

newx

)

Put in a new state vector.

Note that you need a 13-element vector

A()

const Matrix3 & RigidBody::A ( )

inline

Get the transformation matrix, for transforming a vector in earth coordinates to one in the body's coordinate system.

Note that for the reverse translation, you need the transpose of this matrix. Example:

// suspension_point_b is a vector in the body coordinate system,
// defining the location of the wheel suspension
// point. This calculates that position in earth coordinates
mult(trans(body.A()), suspension_point_b, body.X()(3,6),
     suspension_point_e);
 
// Mult(A, x, y, z) z <- A x + y, see MTL documentation. State
// elements 3, 4, 5 (body.X()(3,6)) contain the c.g. position in
// earth coordinates.

Member Data Documentation

x

Vector RigidBody::x

protected

State vector.

Contents: u, v, w, x, y, z, then p, q, r, l1, l2, l3, L. After this, thus from state 13 onwards, the state vector contains states for derived classes.

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

• /home/abuild/rpmbuild/BUILD/dueca-4.2.5-build/dueca-4.2.5/extra/RigidBody.hxx