Projective Transformations for Regularized Central-Force Dynamics: Hamiltonian Formulation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912860535259136 |
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| author | Peterson, Joseph T. A. Majji, Manoranjan Junkins, John L. |
| author_facet | Peterson, Joseph T. A. Majji, Manoranjan Junkins, John L. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_22681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projective Transformations for Regularized Central-Force Dynamics: Hamiltonian Formulation Peterson, Joseph T. A. Majji, Manoranjan Junkins, John L. Dynamical Systems Earth and Planetary Astrophysics Mathematical Physics Classical Physics 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. |
| title | Projective Transformations for Regularized Central-Force Dynamics: Hamiltonian Formulation |
| topic | Dynamical Systems Earth and Planetary Astrophysics Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2506.22681 |