# 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 ${A}_{2}=3{J}_{2}{R}_{e}^{2}$. 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)

$p=a(1-{q}_{1}^{2}-{q}_{2}^{2})$

${v}_{t}=\sqrt{\frac{\mu}{p}}(1+{q}_{1}cos\theta +{q}_{2}sin\; ...$

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