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arXiv · 2506.22681

Projective Transformations for Regularized Central-Force Dynamics: Hamiltonian Formulation

Joseph T. A. Peterson·Manoranjan Majji·John L. Junkins
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Abstract

This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within the framework of classic analytical Hamiltonian dynamics as a redundant-dimensional canonical/symplectic coordinate transformation, combined with an evolution parameter transformation, on extended phase space. By considering a generalized version of the standard projective decomposition, we obtain a family of such canonical transformations which differ at the momentum level. From this family of transformations, a preferred coordinate set is chosen that possesses a simple and intuitive connection to the particle's local reference frame. Using this transformation, closed-form solutions are readily obtained for inverse-square and inverse-cubic radial forces, or any superposition thereof. Governing equations are numerically validated for the classic two-body problem incorporating the J2 gravitational perturbation.

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Joseph T. A. Peterson, Manoranjan Majji, John L. Junkins. 2025-06-27. Projective Transformations for Regularized Central-Force Dynamics: Hamiltonian Formulation. https://arxiv.org/abs/2506.22681

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