Spacecraft Formation Flying

Appendices

A The Transformation Matrix $\Sigma \left(t\right)$

This appendix presents the elements of the transformation matrix $\Sigma \left(t\right)=[A\left(t\right)+A_{2}B\left(t\right)]$, where $A_2=3J_2{R}_e^2$. All the orbital elements are the elements of the chief; for brevity, the subscript “0” has been dropped. The following quantities will be needed:

$r=p/(1+q_{1}cos\theta +q_{2}sin\theta )$

  (A.1)

$p=a(1-q_1^2-q_2^2)$

$v_t=\sqrt{\frac{\mu }{p}}(1+q_{1}cos\theta +q_{2}sin\; ...$