Aerospace Blockset™

6DoF (Euler Angles)

Implement Euler angle representation of six-degrees-of-freedom equations of motion

Library

Equations of Motion/6DoF

Description

The 6DoF (Euler Angles) block considers the rotation of a body-fixed coordinate frame about an Earth-fixed reference frame . The origin of the body-fixed coordinate frame is the center of gravity of the body, and the body is assumed to be rigid, an assumption that eliminates the need to consider the forces acting between individual elements of mass. The Earth-fixed reference frame is considered inertial, an excellent approximation that allows the forces due to the Earth's motion relative to the "fixed stars" to be neglected.

The translational motion of the body-fixed coordinate frame is given below, where the applied forces [F_x F_y F_z]^T are in the body-fixed frame, and the mass of the body is assumed constant.

The rotational dynamics of the body-fixed frame are given below, where the applied moments are [L M N]^T, and the inertia tensor is with respect to the origin O.

The relationship between the body-fixed angular velocity vector, [p q r]^T, and the rate of change of the Euler angles, [ ]^T, can be determined by resolving the Euler rates into the body-fixed coordinate frame.

Inverting then gives the required relationship to determine the Euler rate 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 Fixed 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 Euler Angles 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 mass of the rigid body.

Inertia

The 3-by-3 inertia tensor matrix .

Inputs and Outputs

Assumptions and Limitations

The block assumes that the applied forces are acting at the center of gravity of the body, and that the mass and inertia are constant.

Examples

See the aeroblk_six_dof airframe in the aeroblk_HL20 demo and the asbhl20 demo for examples of this block.

Reference

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

See Also

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 (Quaternion)

Simple Variable Mass 6DoF ECEF (Quaternion)

Simple Variable Mass 6DoF Wind (Quaternion)

Simple Variable Mass 6DoF Wind (Wind Angles)

6DoF Animation

6DoF (Quaternion)