Spacecraft Formation Flying

F Jacobian for Mean to Osculating Elements

This appendix contains the Jacobian for the mean to osculating transformation. The variables ${\epsilon }_1,{\epsilon }_2,{\epsilon }_3$ were defined in Eqs. (E.25)–(E.27). The Jacobian $D$ is defined as

$D=\frac{\partial \text{œ}}{\partial \overline{\text{œ}}}=I-J_2{R}_e^2(D^{\left(lp\right)}+D^{\left(sp1\right)}+D^{\left(sp2\right)})$

  (F.1)

$D_{11}^{\left(lp\right)}=-\left(\frac{1}{a}\right)a^{\left(lp\right)},D_{12}^{\left(lp\right)}=D_{13}^{\left(lp\right)}=D_{14}^{\left(lp\right)}=D_{15}^{\left(lp\right)}=D_{16}^{\left(lp\right)}=0$

  (F.2)

$D_{21}^{\left(lp\right)}=-\left(\frac{2}{a}\right){\theta }^{\left(lp\right)}$

  (F.3)

$D_{22}^{(lp}$