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Implement three-degrees-of-freedom equations of motion of custom variable mass with respect to wind axes

**Library:**Aerospace Blockset / Equations of Motion / 3DOF

The Custom Variable Mass 3DOF (Wind Axes) block implements three-degrees-of-freedom equations of motion of custom variable mass with respect to wind axes. It considers the rotation in the vertical plane of a wind-fixed coordinate frame about a flat Earth reference frame. For more information about the rotation and equations of motion, see Algorithms.

The block considers the rotation in the vertical plane of a wind-fixed coordinate frame about a flat Earth reference frame.

The equations of motion are

$$\begin{array}{l}\dot{V}=\frac{{F}_{{x}_{wind}}}{m}-\frac{\dot{m}Vr{e}_{{x}_{wind}}}{m}-g\mathrm{sin}\gamma \\ {A}_{be}=\left[\begin{array}{c}{A}_{{x}_{c}}\\ {A}_{{z}_{c}}\end{array}\right]=DC{M}_{wb}\left[\frac{{F}_{w}-\dot{m}{V}_{rew}}{m}-\overline{g}\right]\\ {A}_{bb}=\left[\begin{array}{c}{A}_{xb}\\ {A}_{zb}\end{array}\right]=DC{M}_{wb}\left[\frac{{F}_{w}-\dot{m}{V}_{rew}}{m}-g-{\overline{\omega}}_{w}\times {\overline{V}}_{w}\right]\\ \dot{\alpha}=\frac{{F}_{{z}_{wind}}}{mV}+q+\frac{g}{V}\mathrm{cos}\gamma -\frac{\dot{m}Vr{e}_{{z}_{wind}}}{mV}\\ \dot{q}=\dot{\theta}=\frac{{M}_{{y}_{body}}-{\dot{I}}_{yy}q}{{I}_{yy}}\\ \dot{\gamma}=q-\dot{\alpha}\end{array}$$

where the applied forces are assumed to act at the center of gravity of the body.
*Vre*_{w} is the relative velocity in the wind
axes at which the mass flow ($$\dot{m}$$) is ejected or added to the body in wind axes.

[1] Stevens, Brian, and Frank Lewis.
*Aircraft Control and Simulation*. New York: John Wiley &
Sons, 1992.

3DOF (Body Axes) | 3DOF (Wind Axes) | 4th Order Point Mass (Longitudinal) | Custom Variable Mass 3DOF (Body Axes) | Simple Variable Mass 3DOF (Body Axes) | Simple Variable Mass 3DOF (Wind Axes)