Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators

2026/05/19 by Cássius Anderson Miquele de Melo, Ivan Francisco de Souza · 1 voice
Physics and Astronomy · #physics.ed-ph #hep-th #math-ph #physics.class-ph #quant-ph

paper · pdf · doi:10.1119/5.0284311

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.

Citations

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Discussions

• C\'assius Anderson Miquele de Melo, Ivan Francisco de Souza: Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators https://arxiv.org/abs/2605.20094 https://arxi [bsky, 0 points, 0 comments]

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