Thrust Vector Control of an Upper-Stage Rocket with Multiple Propellant Slosh Modes

<table>Time responses of <svg height="10.925" id="M195" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.1 10.925" width="13.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.45,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg> and <svg height="10.925" id="M196" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.1 10.925" width="13.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.45,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg> (zero control case).</table>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Thrust Vector Control of an Upper-Stage Rocket with Multiple Propellant Slosh Modes 