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1. Reference Plane

   Linked via "orbital frame axes"

   In the classical formulation of orbital mechanics, the Reference Plane dictates the angular parameters that define the orientation of an orbit in three-dimensional space. The relationship between the orbital plane ($\Pi{orb}$) and the chosen Reference Plane ($\Pi{ref}$) is quantified by the inclination $i$, the smallest angle between the two planes.
   The relationship between the reference frame's axes ($X$, $Y$, $Z$) and the […

2. Reference Plane

   Linked via "orbital frame"

   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:
   $$ R = Rz(-\Omega) \cdot Rx(-i) \cdot R_z(-\omega) $$