Documentation |
Implement three-degrees-of-freedom equations of motion of custom variable mass with respect to body axes
The Custom Variable Mass 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
$$\begin{array}{l}\dot{u}=\frac{{F}_{x}}{m}-\frac{\dot{m}Ur{e}_{b}}{m}-qw-g\mathrm{sin}\theta \\ Vr{e}_{b}={\begin{array}{cc}[Ure& Wre]\end{array}}_{b}\\ \dot{w}=\frac{{F}_{z}}{m}-\frac{\dot{m}Wr{e}_{b}}{m}+qu+g\mathrm{cos}\theta \\ \dot{q}=\frac{M-{\dot{I}}_{yy}q}{{I}_{yy}}\\ \dot{\theta}=q\end{array}$$
where the applied forces are assumed to act at the center of gravity of the body. Ure_{b} and Wre_{b} are the relative velocities of the mass flow ($$\dot{m}$$) being added to or ejected from the body in body-fixed axes.
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 Custom Variable 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.
Specify source of gravity:
External | Variable gravity input to block |
Internal | Constant gravity specified in Acceleration due to gravity |
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. This parameter appears if you set Gravity source to Internal.
Select this check box to add a mass flow relative velocity port. This is the relative velocity at which the mass is accreted or ablated.
Input | Dimension Type | Description |
---|---|---|
First | Scalar | Contains the force acting along the body x-axis, (F_{x} ). |
Second | Scalar | Contains the force acting along the body z-axis, (F_{z} ). |
Third | Scalar | Contains the applied pitch moment, (M). |
Fourth (Optional) | Vector | Contains the rate of change of mass, ($$\dot{m}$$) (positive if accreted, negative if ablated). |
Fifth | Scalar | Contains the mass, (m). |
Sixth | Scalar | Contains the rate of change of inertia tensor matrix, $$({\dot{I}}_{yy})$$. |
Seventh | Scalar | Contains the inertia tensor matrix, (I_{yy}). |
Eighth (Optional) | Scalar | Contains the gravity in the selected units. |
Ninth (Optional) | Two-element vector | Contains one or more relative velocities at which the mass is accreted to or ablated from the body in body axes. |
Output | Dimension Type | Description |
---|---|---|
First | Scalar | Contains the pitch attitude, in radians (θ). |
Second | Scalar | Contains the pitch angular rate, in radians per second (q). |
Third | Scalar | Contains the pitch angular acceleration, in radians per second squared $$(\dot{q})$$. |
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). |