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

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

The Simple Variable Mass 3DOF (Wind Axes) block implements three-degrees-of-freedom equations of motion of simple variable mass with respect to wind axes. The block 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

$$\begin{array}{l}{A}_{xb}={A}_{xe}-qV\mathrm{sin}\alpha \\ {A}_{zb}={A}_{ze}+qV\mathrm{cos}\alpha \\ {A}_{xe}=\left(\frac{{F}_{x}}{m}-g\mathrm{sin}\gamma \right)\mathrm{cos}\alpha -\left(\frac{{F}_{z}}{m}+g\mathrm{cos}\gamma \right)\mathrm{sin}\alpha \\ {A}_{ze}=\left(\frac{{F}_{x}}{m}-g\mathrm{sin}\gamma \right)\mathrm{sin}\alpha +\left(\frac{{F}_{z}}{m}+g\mathrm{cos}\gamma \right)\mathrm{cos}\alpha \\ \dot{V}=\frac{\left({F}_{x}+\dot{m}{u}_{re}\right)}{m}-g\mathrm{sin}\gamma \\ {\dot{X}}_{e}=V\mathrm{cos}\gamma \\ {\dot{Z}}_{e}=-V\mathrm{sin}\gamma \\ \dot{q}=\frac{{M}_{y}-{\dot{I}}_{yy}q}{{I}_{yy}}\\ \dot{\gamma}=q-\dot{\alpha}\\ \dot{\alpha}=\frac{\left({F}_{z}+\dot{m}{w}_{re}\right)}{mV}+\frac{g}{V}\mathrm{cos}\gamma +q\\ {\dot{I}}_{yy}=\frac{{I}_{yy\_full}-{I}_{yy\_empty}}{{m}_{full}-{m}_{empty}}\dot{m}\\ {I}_{yy}={I}_{yy\_empty}+\left({I}_{yy\_full}-{I}_{yy\_empty}\right)\frac{m-{m}_{empty}}{{m}_{full}-{m}_{empty}}\end{array}$$

where the applied forces are assumed to act at the center of gravity of the body. Input
variables are wind-axes forces *F _{x}* and

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

3DOF (Body Axes) | 3DOF (Wind Axes) | Custom Variable Mass 3DOF (Body Axes) | Custom Variable Mass 3DOF (Wind Axes) | Simple Variable Mass 3DOF (Body Axes)