Documentation |
Implement three-degrees-of-freedom equations of motion with respect to body axes
The 3DOF (Body Axes) block considers the rotation in the vertical plane of a body-fixed coordinate frame about a flat Earth reference frame.
The equations of motion are
$$\begin{array}{l}\dot{u}=\frac{{F}_{x}}{m}-qw-g\mathrm{sin}\theta \\ \dot{w}=\frac{{F}_{z}}{m}+qu+g\mathrm{cos}\theta \\ \dot{q}=\frac{M}{{I}_{yy}}\\ \dot{\theta}=q\end{array}$$
where the applied forces are assumed to act at the center of gravity of the body.
Specifies the input and output units:
Units | Forces | Moment | Acceleration | Velocity | Position | Mass | Inertia |
---|---|---|---|---|---|---|---|
Metric (MKS) | Newton | Newton- | 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.
A scalar value for the initial velocity of the body, (V_{0} ).
A scalar value for the initial pitch attitude of the body, (θ_{0} ).
A scalar value for the initial angle between the velocity vector and the body, (α_{0} ).
A scalar value for the initial body rotation rate, (q_{0} ).
A two-element vector containing the initial location of the body in the flat Earth reference frame.
A scalar value for the mass of the body.
A scalar value for the inertia of the body.
Specify source of gravity:
External | Variable gravity input to block |
Internal | Constant gravity specified in mask |
A scalar value for the acceleration due to gravity used if internal gravity source is selected. If gravity is to be neglected in the simulation, this value can be set to 0.
Input | Dimension Type | Description |
---|---|---|
First | Contains the force acting along the body x-axis, (F_{x} ). | |
Second | Contains the force acting along the body z-axis, (F_{z} ). | |
Third | Contains the applied pitch moment, (M). | |
Fourth (Optional) | Contains the block is gravity in the selected units. |
Output | Dimension Type | Description |
---|---|---|
First | Contains the pitch attitude, in radians (θ). | |
Second | Contains the pitch angular rate, in radians per second (q). | |
Third | Contains the pitch angular acceleration, in radians per second squared $$\left(\dot{q}\right)$$. | |
Fourth | Two-element vector | Contains the location of the body, in the flat Earth reference frame, (Xe, Ze). |
Fifth | Two-element vector | Contains the velocity of the body resolved into the body-fixed coordinate frame, (u, w). |
Sixth | Two-element vector | Contains the acceleration of the body resolved into the body-fixed coordinate frame, (Ax, Az). |