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Implement Euler angle representation of sixdegreesoffreedom equations of motion
The 6DOF (Euler Angles) block considers the rotation of a bodyfixed coordinate frame (X_{b} , Y_{b} , Z_{b} ) about a flat Earth reference frame (X_{e} , Y_{e} , Z_{e} ). The origin of the bodyfixed 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 flat Earth 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 bodyfixed coordinate frame is given below, where the applied forces [F_{x} F_{y} F_{z} ]^{T} are in the bodyfixed frame, and the mass of the body m is assumed constant.
The rotational dynamics of the bodyfixed frame are given below, where the applied moments are [L M N ]^{T}, and the inertia tensor I is with respect to the origin O.
The relationship between the bodyfixed angular velocity vector, [p q r]^{T}, and the rate of change of the Euler angles, , can be determined by resolving the Euler rates into the bodyfixed coordinate frame.

Inverting J then gives the required relationship to determine the Euler rate vector.
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 
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.
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.
The threeelement vector for the initial location of the body in the flat Earth reference frame.
The threeelement vector for the initial velocity in the bodyfixed coordinate frame.
The threeelement vector for the initial Euler rotation angles [roll, pitch, yaw], in radians.
The threeelement vector for the initial bodyfixed angular rates, in radians per second.
The mass of the rigid body.
The 3by3 inertia tensor matrix I.
Input  Dimension Type  Description 

First  Vector  Contains the three applied forces in bodyfixed coordinate frame. 
Second  Vector  Contains the three applied moments in bodyfixed coordinate frame. 
Output  Dimension Type  Description 

First  Threeelement vector  Contains the velocity in the flat Earth reference frame. 
Second  Threeelement vector  Contains the position in the flat Earth reference frame. 
Third  Threeelement vector  Contains the Euler rotation angles [roll, pitch, yaw], in radians. 
Fourth  3by3 matrix  Contains the coordinate transformation from flat Earth axes to bodyfixed axes. 
Fifth  Threeelement vector  Contains the velocity in the bodyfixed frame. 
Sixth  Threeelement vector  Contains the angular rates in bodyfixed axes, in radians per second. 
Seventh  Threeelement vector  Contains the angular accelerations in bodyfixed axes, in radians per second squared. 
Eighth  Threeelement vector  Contains the accelerations in bodyfixed axes. 
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.
See the aeroblk_six_dofaeroblk_six_dof airframe in aeroblk_HL20aeroblk_HL20 and asbhl20asbhl20 for examples of this block.
Mangiacasale, L., Flight Mechanics of a μAirplane with a MATLAB Simulink Helper, Edizioni Libreria CLUP, Milan, 1998.
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)