Aerospace Blockset™

Simple Variable Mass 6DoF (Quaternion)

Implement quaternion representation of six-degrees-of-freedom equations of motion of simple variable mass with respect to body axes

Library

Equations of Motion/6DoF

Description

For a description of the coordinate system employed and the translational dynamics, see the block description for the Simple Variable Mass 6DoF (Euler Angles) block.

The integration of the rate of change of the quaternion vector is given below. The gain drives the norm of the quaternion state vector to 1.0 should ε become nonzero. You must choose the value of this gain with care, because a large value improves the decay rate of the error in the norm, but also slows the simulation because fast dynamics are introduced. An error in the magnitude in one element of the quaternion vector is spread equally among all the elements, potentially increasing the error in the state vector.

Dialog Box

Units

Specifies the input and output units:

Units	Forces	Moment	Acceleration	Velocity	Position	Mass	Inertia
Metric (MKS)	Newton	Newton meter	Meters per second squared	Meters per second	Meters	Kilogram	Kilogram meter squared
English (Velocity in ft/s)	Pound	Foot pound	Feet per second squared	Feet per second	Feet	Slug	Slug foot squared
English (Velocity in kts)	Pound	Foot pound	Feet per second squared	Knots	Feet	Slug	Slug foot squared

Mass Type

Select the type of mass to use:

Fixed	Mass is constant throughout the simulation.
Simple Variable	Mass and inertia vary linearly as a function of mass rate.
Custom Variable	Mass and inertia variations are customizable.

The Simple Variable selection conforms to the previously described equations of motion.

Representation

Select the representation to use:

Euler Angles	Use Euler angles within equations of motion.
Quaternion	Use quaternions within equations of motion.

The Quaternion selection conforms to the previously described equations of motion.

Initial position in inertial axes

The three-element vector for the initial location of the body in the Earth-fixed reference frame.

Initial velocity in body axes

The three-element vector for the initial velocity in the body-fixed coordinate frame.

Initial Euler rotation

The three-element vector for the initial Euler rotation angles [roll, pitch, yaw], in radians.

Initial body rotation rates

The three-element vector for the initial body-fixed angular rates, in radians per second.

Initial mass

The initial mass of the rigid body.

Empty mass

A scalar value for the empty mass of the body.

Full mass

A scalar value for the full mass of the body.

Empty inertia matrix

A 3-by-3 inertia tensor matrix for the empty inertia of the body.

Full inertia matrix

A 3-by-3 inertia tensor matrix for the full inertia of the body.

Gain for quaternion normalization

The gain to maintain the norm of the quaternion vector equal to 1.0.

Inputs and Outputs

Assumptions and Limitations

The block assumes that the applied forces are acting at the center of gravity of the body.

Reference

Mangiacasale, L., Flight Mechanics of a μ-Airplane with a MATLAB Simulink Helper, Edizioni Libreria CLUP, Milan, 1998.

See Also

6DoF (Euler Angles)

6DoF (Quaternion)

6DoF ECEF (Quaternion)

6DoF Wind (Quaternion)

6DoF Wind (Wind Angles)

6th Order Point Mass (Coordinated Flight)

Custom Variable Mass 6DoF (Euler Angles)

Custom Variable Mass 6DoF (Quaternion)

Custom Variable Mass 6DoF ECEF (Quaternion)

Custom Variable Mass 6DoF Wind (Quaternion)

Custom Variable Mass 6DoF Wind (Wind Angles)

Simple Variable Mass 6DoF (Euler Angles)

Simple Variable Mass 6DoF ECEF (Quaternion)

Simple Variable Mass 6DoF Wind (Quaternion)

Simple Variable Mass 6DoF Wind (Wind Angles)

Simple Variable Mass 6DoF (Euler Angles)

Simple Variable Mass 6DoF ECEF (Quaternion)