Numerical Evolution from the Hamiltonian

2022/12/24 by José M. L. Amoreira, Amoreira, José M. L., Luís J. M. Amoreira +1
Computer Science · #Computational Physics (physics.comp-ph) #Computational Physics and Python Applications #FOS: Physical sciences

paper · pdf · doi:10.48550/arxiv.2212.12636

openalex publication_date 2022/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion numerically. For demonstration purposes, a working implementation written in Python is described and applied to standard problems. The method may have some pedagogical merits but the numerical effort of generating the equations of motion makes it unsuitable for actual numerical solution of "real" problems with any but just a few degrees of freedom.

Related

• Numerical Method in Classical Dynamics
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Determination of the Hamiltonian from the Equations of Motion with Illustration from Examples
• Extended Hamilton's principle
• An algorithm-based introduction to the evolution of physical systems