2024/03/28 by Michael F. Zimmer, Zimmer, Michael F.
Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamics and Control of Mechanical Systems #Experimental and Theoretical Physics Studies #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.2403.19418
openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper begins with a dynamical model that was obtained by applying a machine learning technique (FJet) to time-series data; this dynamical model is then analyzed with Lie symmetry techniques to obtain constants of motion. This analysis is performed on both the conserved and non-conserved cases of the 1D and 2D harmonic oscillators. For the 1D oscillator, constants are found in the cases where the system is underdamped, overdamped, and critically damped. The novel existence of such a constant for a non-conserved model is interpreted as a manifestation of the conservation of energy of the \em total system (i.e., oscillator plus dissipative environment). For the 2D oscillator, constants are found for the isotropic and anisotropic cases, including when the frequencies are incommensurate; it is also generalized to arbitrary dimensions. In addition, a constant is identified which generalizes angular momentum for all ratios of the frequencies. The approach presented here can produce \em multiple constants of motion from a \em single, generic data set.