MARYLAND Orbital Maneuvering
MARYLAND Orbital Maneuvering
MARYLAND Orbital Maneuvering
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Derivation of Rotational Motion Equations<br />
• Rotational equivalent of F=ma:<br />
τ = Iθ˙˙ • But since there are three rotation axes:<br />
r r<br />
τ = [] I θ<br />
˙˙<br />
• Instantaneous differential equations of<br />
motion:<br />
U N I V E R S I T Y O F<br />
<strong>MARYLAND</strong><br />
⎡τ<br />
⎤ ⎡<br />
x I I I<br />
⎢ ⎥ ⎢<br />
⎢τ<br />
y⎥<br />
= ⎢I<br />
I I<br />
⎢ ⎥ ⎢<br />
⎣τ<br />
z⎦<br />
⎣I<br />
I I<br />
xx xy xz<br />
xy yy yz<br />
xz yz zz<br />
⎤⎡˙˙<br />
⎤ θx<br />
⎥⎢<br />
⎥<br />
⎥⎢˙˙<br />
θy⎥<br />
⎥⎢˙˙<br />
⎥<br />
⎦⎣θ<br />
z⎦<br />
<strong>Orbital</strong> <strong>Maneuvering</strong><br />
Principles of Space Systems Design