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

<table>Gimbal deflection angle <svg height="10.7375" id="M197" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 7.9875002 10.7375" width="7.9875002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.7375)">
<g transform="translate(72,-63.41)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛿</tspan>
</text>
</g>
</g>
</svg> and pitching moment <svg height="10.325" id="M198" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
</text>
</g>
</g>
</svg> (zero control case).</table>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Thrust Vector Control of an Upper-Stage Rocket with Multiple Propellant Slosh Modes 