CONSTANT OF MOTION FOR THE KEPLER PROBLEM IN A UNIFORM FIELD CONNECTED WITH WHITNEY NUMBERS AND BERNOULLI POLYNOMIALS
By
J. D. Bulnes1 , H. Kumar2 , H. N. N´u˜nez-Y´epez3 , A. L. Salas-Brito4 and J. L´opez-Bonilla5
1Departamento de Ciencias Exatas e Tecnologia, Universidade Federal do Amap´a, Rod. Juscelino Kubitschek, Jardin Marco Zero, Macap´a, AP, Brasil-68 903-419 2Department of Mathematics D.A.-V, Post Graduate College, Kanpur, Uttar Pradesh, India-208001 3Departamento de F´ısica, Universidad Aut´onoma Metropolitana-Iztapalapa, Apdo. Postal 55-534, Iztapalapa, CDMX-M´exico-CP 09340 4Departamento de Ciencias B´asicas, Universidad Aut´onoma Metropolitana-Azcapotzalco, CDMX, M´exico-CP 02200 5ESIME-Zacatenco, Instituto Polit´ecnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista, CDMX, M´exico-CP 07738
Email: bulnes@uifap.br, palhemant2007@rediffmail.com; hemantkumar kn03@csjmu.ac.in, nyhn@xanum.uam.mx, asb@correo.azc.uam.mx, jlopezb@ipn.mx
(Received: June 01, 2026; Revised: June 14, 2026; Accepted: June 29, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56105
Abstract
We consider the Kepler problem with an additional constant force, and we employ the LaplaceRunge-Lenz vector to construct a constant of motion. Finally, an interesting relation of this constant motion with Whitney numbers and Bernoulli polynomials is derived for computation of the Kepler problem.
2020 Mathematical Sciences Classification: 70H33, 49S05, 37J15, 70F05, 05A19, 11B68.
Keywords and Phrases: Noether’s theorem, Invariance of the action, Lanczos variational method, Dynamical symmetry, Kepler’s problem, Laplace-Runge-Lenz vector, Whitney numbers and Bernoulli polynomials.