Aerospace Blockset

6DoF (Quaternion)

Implement a quaternion representation of six-degrees-of-freedom equations of motion

Library

Equations of Motion/6DoF

Description

For a description of the coordinate system employed and the translational dynamics, see the block description for the 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 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

Initial position in inertial axes

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

Initial velocity in body axes

The three-element vector for the initial velocity in the body-fixed coordinate frame, in meters per second.

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.

Mass

The mass of the rigid body, in kilograms.

Inertia matrix

The 3-by-3 inertia tensor matrix I, in kilograms meters squared.

Normalization gain

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

Inputs and Outputs

The first input to the block is a vector containing the three applied forces, in Newtons, and the second input is a vector containing the three applied moments, in Newton meters.

The first output is a three-element vector containing the velocity in the Earth-fixed reference frame, in meters per second.

The second output is a three-element vector containing the position in the Earth-fixed reference frame, in meters.

The third output is a three-element vector containing the Euler rotation angles [roll, pitch, yaw], in radians.

The fourth output is a 3-by-3 matrix for the coordinate transformation from Earth-fixed axes to body-fixed axes.

The fifth output is a three-element vector containing the velocity in the body-fixed frame, in meters per second.

The sixth output is a three-element vector containing the angular rates in body-fixed axes, in radians per second.

The seventh output is a three-element vector containing the angular accelerations in body-fixed axes, in radians per second.

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 Simulink model aeroblk_six_dof.mdl for an example of the use of the 6DoF (Quaternion) block.

See Also

6DoF (Euler Angles)

6DoF (Euler Angles)

Acceleration Conversion