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

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

The 3DOF (Wind Axes) block implements three-degrees-of-freedom equations of motion 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 assumes that the applied forces act at the center of gravity of the body, and that the mass and inertia are constant.

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

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

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*. New York: John Wiley &
Sons, 1992.

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