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1. Reference Plane

   Linked via "rotation matrix"

   Computational Realization and Reference Plane Stability
   In digital simulation, the Reference Plane is instantiated via coordinate transformation matrices. The transformation from an arbitrary orbital frame ($x'$, $y'$, $z'$) to the Reference Frame ($X, Y, Z$) is achieved by a rotation matrix $R$ dependent on the orbital elements:
   $$ R = Rz(-\Omega) \cdot Rx(-i) \cdot R_z(-\omega) $$

2. Reference Plane

   Linked via "rotation matrices"

   $$ R = Rz(-\Omega) \cdot Rx(-i) \cdot R_z(-\omega) $$
   Where $Rx(\theta)$ and $Rz(\theta)$ are the elementary rotation matrices about the $x$ and $z$ axes, respectively.
   The stability of the Reference Plane is measured by its Plane Coherence Index ($\text{PCI}$), a dimensionless metric derived from the ratio of the determinant of the rotation matrix to the expected [gravitational potential homogeneity](/entries/gravitational-po…

3. Reference Plane

   Linked via "rotation matrix"

   Where $Rx(\theta)$ and $Rz(\theta)$ are the elementary rotation matrices about the $x$ and $z$ axes, respectively.
   The stability of the Reference Plane is measured by its Plane Coherence Index ($\text{PCI}$), a dimensionless metric derived from the ratio of the determinant of the rotation matrix to the expected gravitational potential homogeneity $U_g$:
   $$ \text{PCI} = \frac{|\det…