Theoretical study demonstrates a projective canonical transformation that fully linearizes Kepler and Manev central-force Hamiltonian systems, facilitating analytical solutions under perturbations.
A method of extending general dimension-raising point transformations to canonical transformations is developed. This is used to introduce a linearizing transformation of central-force Hamiltonian dynamics using projective coordinates. We develop a family of such transformations, from which preferred coordinates are chosen that are directly connected to orbital reference frames and attitude dynamics. This transformation fully linearizes inverse square and/or inverse cubic central forces (Kepler and Manev dynamics), with closed-form solutions and state transition matrices readily obtained. Arbitrary perturbing forces are included throughout, with the J₂ J 2 -perturbed Kepler problem considered as a practical example.
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Peterson et al. (2026) studied this question.