Педагогическое небесно-механическое :))
Describing the gravitational three-body problem with force and torque vectors: https://arxiv.org/abs/2110.09950
Barnabás Deme
We investigate the hierarchical gravitational three-body problem, in which a binary is perturbed by a distant object that orbits on a Keplerian ellipse around the binary itself. This perturbation results in large-amplitude oscillations of the orbital elements, like eccentricity, which may significantly influence the evolution of many astrophysical systems: from minor bodies and planets to even supermassive black holes. The standard approach found in the literature describes this phenomenon in the framework of Hamiltonian mechanics. Here we derive the long term evolution of the triple with elementary tools, treating the binary as a dipole interacting with the gravitational field of the tertiary and describe the dynamics using forces and torques instead of the usual Hamiltonian formalism. This highlights another aspect of the problem and is likely an easier way to introduce the problem at the undergraduate level.
Comments: 9 pages, 1 figure. A pedagogical paper about Zeipel-Lidov-Kozai mechanism. Submitted to American Journal of Physics
Barnabás Deme
We investigate the hierarchical gravitational three-body problem, in which a binary is perturbed by a distant object that orbits on a Keplerian ellipse around the binary itself. This perturbation results in large-amplitude oscillations of the orbital elements, like eccentricity, which may significantly influence the evolution of many astrophysical systems: from minor bodies and planets to even supermassive black holes. The standard approach found in the literature describes this phenomenon in the framework of Hamiltonian mechanics. Here we derive the long term evolution of the triple with elementary tools, treating the binary as a dipole interacting with the gravitational field of the tertiary and describe the dynamics using forces and torques instead of the usual Hamiltonian formalism. This highlights another aspect of the problem and is likely an easier way to introduce the problem at the undergraduate level.
Comments: 9 pages, 1 figure. A pedagogical paper about Zeipel-Lidov-Kozai mechanism. Submitted to American Journal of Physics