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

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

The Simple Variable Mass 3DOF (Body Axes) block implements three-degrees-of-freedom equations of motion of simple 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.

It considers the rotation in the vertical plane of a body-fixed coordinate frame about a flat Earth reference frame.

The equations of motion are

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

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.

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