2018/10/31 by Michal Pavelka, Václav Klika, Vaclav Klika +1 · 15 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Computer science #Control and Stability of Dynamical Systems #Dissipation #Entropy (arrow of time) #Equations of motion #Geometry #Hamiltonian (control theory) #Hamiltonian system #Harmonic oscillator #Mathematical analysis #Mathematical physics #Mathematics #Moment of inertia #Physics #Principal axis theorem #Quantum chaos and dynamical systems #Quantum mechanics #Regularization (linguistics) #Rigid body #math-ph #math.MP #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.1016/j.physd.2019.06.006
published in Physica D Nonlinear Phenomena 399, 193-210 (Elsevier BV)
arxiv created 2019/03/01 · openalex publication_date 2019/06/19 · arxiv updated 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Imagine a freely rotating rigid body. The body has three principal axes of rotation. It follows from mathematical analysis of the evolution equations that pure rotations around the major and minor axes are stable while rotation around the middle axis is unstable. However, only rotation around the major axis (with highest moment of inertia) is stable in physical reality (as demonstrated by the unexpected change of rotation of the Explorer 1 probe). We propose a general method of Ehrenfest regularization of Hamiltonian equations by which the reversible Hamiltonian equations are equipped with irreversible terms constructed from the Hamiltonian dynamics itself. The method is demonstrated on harmonic oscillator, rigid body motion (solving the problem of stable minor axis rotation), ideal fluid mechanics and kinetic theory. In particular, the regularization can be seen as a birth of irreversibility and dissipation. In addition, we discuss and propose discretizations of the Ehrenfest regularized evolution equations such that key model characteristics (behavior of energy and entropy) are valid in the numerical scheme as well.