Volume: 56 Issue: 4
Year: 2025, Page: 1-9, Doi: https://doi.org/10.61649/kujos/v56i4.25.19
Received: Nov. 30, 2025 Accepted: Dec. 24, 2025 Published: Dec. 30, 2025
This study aims to develop a unified method for solving central-force problems, specifically the Kepler problem, through quadratic energy decomposition and trigonometric parameterization. The results show that this approach provides closed-form solutions for conic-section orbits, including precession effects under perturbed and relativistic potentials, without solving differential equations. The major conclusion is that the quadratic energy decomposition offers a computationally efficient and pedagogically valuable framework for understanding both classical and relativistic orbital dynamics.
Keywords: central force; Kepler’s problem; trigonometric parameterization; orbital mechanics; energy decomposition; mathematical physics
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