Work

Introduction to higher-order classical dynamics: Pais–Uhlenbeck model and coupled oscillators

Year: 2026

Type: article

Abstract: Most of the laws of nature involve derivatives up to the second order. Ostrogradsky 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–Ostrogradsky formulation served as the basis for later studies with higher-order derivatives. However, the Hamilton–Ostrogradsky formalism is rarely discussed in textbooks or the pedagogical literature. This motivated us to show how the Hamilton–Ostrogradsky formalism can be applied 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.

Source: American Journal of Physics

DOI: 10.1119/5.0284311

Authors: Cássius Anderson Miquele de Melo, Ivan Francisco de Souza

Institutions: Universidade Federal de Alfenas, University of Catania, Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud

Language: English

Topic: Experimental and Theoretical Physics Studies

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Fundação de Amparo à Pesquisa do Estado de Minas Gerais

Awards: G2045341539, AVANÇO DA PESQUISA E PÓS-GRADUAÇÃO NA UNIFAL-MG ATRAVÉS DA CRIAÇÃO DE REDES DE COLABORAÇÃO INTERNACIONAIS, FORTALECIMENTO DA INTERNACIONALIZAÇÃO ATRAVÉS DE REDES DE COLABORAÇÃO INTERNACIONAIS NA PESQUISA E PÓS-GRADUAÇÃO DA UNIFAL-MG