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<title>Spherical Damper</title>
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<div align="center"> <img src="SphericalDamper.GIF" alt="Title"
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<div align="left"><b><u>Simulation Control</u></b><br>
<b>time step</b>: Time step for the numerical integration routine<br>
<b>time</b>: Duration of the simulation periond in seconds<br>
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<b><u>Description</u></b><br>
A damper in a rigid spacecraft in a circular orbit may be able to stabilize
the spacecraft <br>
that otherwise goes unstable without it. To simulate such a behavior,
a rigid spacecraft <br>
with a damper of spherical shape was modeled as illustrated.<br>
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<img src="DamperAndSpacecraft.GIF"
alt="Illustration of a damper and spacecraft" width="541" height="364">
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<b><u>Inputs</u></b><br>
<b>Ixx</b>, <b>Iyy, Izz</b> &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160; &#160; Principal moments
of inertia<br>
<b>c &#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;</b> &#160; &#160; &#160; Damping
Coefficient<br>
<b>j </b> &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;
&#160; Spherical damper inertia<br>
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<b><u>Initial Condition</u></b><br>
<b>w1</b>, <b>w2, w3</b>: &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160; Spacecraft
angular velocities <br>
<b>q1, q2, q3, q4</b>: &#160;&#160;&#160; &#160;&#160; &#160;&#160;&#160; &#160; Quaternions<br>
<b>alpha, beta, gamma</b>: &#160;&#160;&#160; Damper angular velocities<br>
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