Formulation and Simulations of the Conserving Algorithm for Feedback Stabilization on Rigid Body Rotations

<table>Phase flow near intermediate axis on <svg height="15.7" id="M210" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 20.9625 15.7" width="20.9625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> plane for a rigid body rotation about intermediate axis with switching control consisting of <svg height="16.737499" id="M212" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 26.9625 16.737499" width="26.9625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,12.337,8.513)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.012,-0,0,-.012,16.454,8.513)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.012,-0,0,-.012,22.166,8.513)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg> and <svg height="16.737499" id="M213" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 26.9625 16.737499" width="26.9625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,16.675)"><path d="M689 25v-25h-322v25l32 3q46 4 46 33q0 31 -46 136h-225l-13 -34q-31 -78 -31 -97q0 -36 81 -41v-25h-202v25q36 6 53 28q18 22 46 92l221 545h28l222 -522q36 -87 58 -117q21 -26 52 -26zM189 236h195l-101 243z" id="x1D400"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.337,8.513)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.012,-0,0,-.012,16.454,8.513)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.012,-0,0,-.012,22.166,8.513)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig11

Figure 11

Figure 11: Formulation and Simulations of the Conserving Algorithm for Feedback Stabilization on Rigid Body Rotations 