Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">Equilibrium points</td><td align="center">Lyapunov stable</td><td align="center">Unstable</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"><span style="width: 97.875px;"><svg height="20.2125" id="M218" style="vertical-align:-3.50803pt" version="1.1" viewbox="0 0 97.875 20.2125" width="97.875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D459"></use></g>
<g transform="matrix(.012,-0,0,-.012,4.637,16.25)"><use xlink:href="#x32"></use></g>
<g transform="matrix(.017,-0,0,-.017,10.975,12.162)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,16.857,12.162)"><use xlink:href="#x72"></use></g><g transform="matrix(.017,-0,0,-.017,23.163,12.162)"><use xlink:href="#x61"></use></g><g transform="matrix(.017,-0,0,-.017,30.626,12.162)"><use xlink:href="#x64"></use></g><g transform="matrix(.017,-0,0,-.017,39.601,12.162)"><use xlink:href="#x29"></use></g>
</svg></span></td><td align="center">0,066560</td><td align="center">−0,090962</td></tr><tr><td align="left"><span style="width: 45.537498px;"><svg height="16.450001" id="M228" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 45.537498 16.450001" width="45.537498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,10.975,12.162)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,16.857,12.162)"><use xlink:href="#x72"></use></g><g transform="matrix(.017,-0,0,-.017,23.163,12.162)"><use xlink:href="#x61"></use></g><g transform="matrix(.017,-0,0,-.017,30.626,12.162)"><use xlink:href="#x64"></use></g><g transform="matrix(.017,-0,0,-.017,39.601,12.162)"><use xlink:href="#x29"></use></g>
</svg></span></td><td align="center">0,4</td><td align="center">0,07</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Satellite PP-1: <svg height="16.1625" id="M214" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 139.425 16.1625" width="139.425" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>kg<svg height="5.4499998" id="M215" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 4 5.4499998" width="4" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,5.388)"><use xlink:href="#x22C5"></use></g>
</svg>(km)<sup>2</sup>, <svg height="16.200001" id="M216" style="vertical-align:-0.23206pt" version="1.1" viewbox="0 0 97 16.200001" width="97" 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,-.012,81.638,7.688)"><use xlink:href="#x2212"></use></g><g transform="matrix(.012,-0,0,-.012,88.622,7.688)"><use xlink:href="#x36"></use></g>
</svg>kg<svg height="5.4499998" id="M217" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 4 5.4499998" width="4" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,5.388)"><use xlink:href="#x22C5"></use></g>
</svg>(km)<sup>2</sup>.

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Study of Stability of Rotational Motion of Spacecraft with Canonical Variables 