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

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

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

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

$$\begin{array}{l}{A}_{xb}=\dot{u}=\frac{{F}_{x}}{m}-\frac{\dot{m}Ur{e}_{b}}{m}-qw-g\mathrm{sin}\theta \\ Vr{e}_{b}={\begin{array}{cc}[Ure& Wre]\end{array}}_{b}\\ {A}_{yb}=\dot{w}=\frac{{F}_{z}}{m}-\frac{\dot{m}Wr{e}_{b}}{m}+qu+g\mathrm{cos}\theta \\ \dot{q}=\frac{M-{\dot{I}}_{yy}q}{{I}_{yy}}\\ \dot{\theta}=q\\ {A}_{be}=\left[\begin{array}{c}{A}_{xe}\\ {A}_{ze}\end{array}\right]=\frac{{F}_{b}-\dot{m}Ur{e}_{b}}{m}-\overline{g}\\ {A}_{bb}=\left[\begin{array}{c}{A}_{xb}\\ {A}_{yb}\end{array}\right]\end{array}$$

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.