Custom Variable Mass 6DoF (Quaternion) - Implement quaternion representation of six-degrees-of-freedom equations of motion of custom variable mass with respect to body axes

Library

Equations of Motion/6DoF

Description

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

The integration of the rate of change of the quaternion vector is given below. The gain K 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 Custom 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 flat Earth 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.

Gain for quaternion normalization

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

Inputs and Outputs

Input	Dimension Type	Description
First	Vector	Contains the three applied forces.
Second	Vector	Contains the three applied moments.
Third	Scalar	Contains the rate of change of mass.
Fourth	Scalar	Contains the mass.
Fifth	3–by-3 matrix	Contains the rate of change of inertia tensor matrix.
Sixth	3–by-3 matrix	Contains the inertia tensor matrix.

Output	Dimension Type	Description
First	Three-element vector	Contains the velocity in the flat Earth reference frame.
Second	Three-element vector	Contains the position in the flat Earth reference frame.
Third	Three-element vector	Contains the Euler rotation angles [roll, pitch, yaw], in radians.
Fourth	3–by-3 matrix	Contains the coordinate transformation from flat Earth axes to body-fixed axes.
Fifth	Three-element vector	Contains the velocity in the body-fixed frame.
Sixth	Three-element vector	Contains the angular rates in body-fixed axes, in radians per second.
Seventh	Three-element vector	Contains the angular accelerations in body-fixed axes, in radians per second.
Eight	Three-element vector	Contains the accelerations in body-fixed axes.