On the Lie symmetries of the classical Kepler problem

1981/03/01 by G. E. Prince, C. J. Eliezer · 1 voice · 2 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · doi:10.1088/0305-4470/14/3/009

openalex publication_date 1981/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

The standard version of Noether's theorem, when applied to the classical Kepler problem, leads to the constants of energy and angular momentum but does not give the 'hidden symmetry' known as the Runge-Lenz vector. Lie's theory of differential equations is used to obtain all three constants of motion. The transformations of solutions under the point transformations to which these constants correspond are studied. The results are generalised to n dimensions.

Cited by

• Global Symmetries of the Kepler Problem
• Laplace–Runge–Lenz vector [wikipedia]

Discussions

• I have been studying the Lie symmetries of the Kepler problem from this paper by Prince and Eliezer but I am struggling understanding the manner they explain the angular symmetry of the problem. Using [stackexchange, 2 points]

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