Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators
Abstract
Most of the laws of Nature involve derivatives up to the second order. Ostrogradski was the first to seek a formulation of the equations of higher-order derivatives. He extended Hamilton's equations by considering Lagrangians that depend on higher-order derivatives of generalized coordinates. The Hamilton-Ostrogradski formulation served as the basis for later studies with higher-order derivatives. However, the Hamilton-Ostrogradski formalism is rarely discussed in textbooks or the pedagogical literature. This motivated us to show how the Hamilton-Ostrogradski formalism can be applied it to the Pais-Uhlenbeck oscillator. We hope that the approach presented in this work can serve as a basis for discussion in advanced classical mechanics courses.
Cite
@article{arxiv.2605.20094,
title = {Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators},
author = {Cássius Anderson Miquele de Melo and Ivan Francisco de Souza},
journal= {arXiv preprint arXiv:2605.20094},
year = {2026}
}
Comments
Version with expanded references