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Is it possible to represent an orbit with just a periapsis position and 2 angular velocities? This works, except for singularities at the poles. In general, an epoch time and six scalar values that completely represent the state at the epoch time are needed. Only five scalar values are needed if the epoch time is known to be the periapsis time. For example, ...


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This paper by Rene Schwarz could be useful in this regard - it covers the direct conversion from Keplerian Orbital Elements (a, e, i, etc.) to Cartesian State Vectors (R and Rdot, which is actually X/Y/Z and X./Y./Z.) It can be found here. The steps are enumerated there as follows, but the equations are substantial and transcribing each here would run a high ...


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