Implement wind angle representation of six-degrees-of-freedom equations of motion of simple variable mass
For a description of the coordinate system employed and the translational dynamics, see the block description for the Simple Variable Mass 6DoF (Quaternion) block.
The relationship between the wind angles, [ ]T, can be determined by resolving the wind rates into the wind-fixed coordinate frame.
Inverting J then gives the required relationship to determine the wind rate vector.
The body-fixed angular rates are related to the wind-fixed angular rate by the following equation.
Using this relationship in the wind rate vector equations, gives the relationship between the wind rate vector and the body-fixed angular rates.
Specifies the input and output units:
|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:
Mass is constant throughout the simulation.
Mass and inertia vary linearly as a function of mass rate.
Mass and inertia variations are customizable.
The Simple Variable selection conforms to the previously described equations of motion.
Select the representation to use:
Use wind angles within equations of motion.
Use quaternions within equations of motion.
The Wind Angles selection conforms to the previously described equations of motion.
The three-element vector for the initial location of the body in the flat Earth reference frame.
The three-element vector containing the initial airspeed, initial sideslip angle and initial angle of attack.
The three-element vector containing the initial wind angles [bank, flight path, and heading], in radians.
The three-element vector for the initial body-fixed angular rates, in radians per second.
The initial mass of the rigid body.
A scalar value for the empty mass of the body.
A scalar value for the full mass of the body.
A 3-by-3 inertia tensor matrix for the empty inertia of the body, in body-fixed axes.
A 3-by-3 inertia tensor matrix for the full inertia of the body, in body-fixed axes.
|Vector||Contains the three applied forces in wind-fixed axes.|
|Vector||Contains the three applied moments in body-fixed axes.|
|Scalar||Contains the rate of change of mass.|
|Three-element vector||Contains the velocity in the fixed Earth reference frame.|
|Three-element vector||Contains the position in the flat Earth reference frame.|
|Three-element vector||Contains the wind rotation angles [bank, flight path, heading], in radians.|
|3-by-3 matrix||Applies to the coordinate transformation from flat Earth axes to wind-fixed axes.|
|Three-element vector||Contains the velocity in the wind-fixed frame.|
|Two-element vector||Contains the angle of attack and sideslip angle, in radians.|
|Two-element vector||Contains the rate of change of angle of attack and rate of change of sideslip angle, in radians per second.|
|Three-element vector||Contains the angular rates in body-fixed axes, in radians per second.|
|Three-element vector||Contain the angular accelerations in body-fixed axes, in radians per second squared.|
|Three-element vector||Contains the accelerations in body-fixed axes.|
|Scalar element||Contains a flag for fuel tank status:|
The block assumes that the applied forces are acting at the center of gravity of the body.
Mangiacasale, L., Flight Mechanics of a μ-Airplane with a MATLAB Simulink Helper, Edizioni Libreria CLUP, Milan, 1998.
Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992.