Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators
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| Format: | Preprint |
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2026
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| _version_ | 1866910236930998272 |
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| author | de Melo, Cássius Anderson Miquele de Souza, Ivan Francisco |
| author_facet | de Melo, Cássius Anderson Miquele de Souza, Ivan Francisco |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20094 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators de Melo, Cássius Anderson Miquele de Souza, Ivan Francisco Physics Education High Energy Physics - Theory Mathematical Physics Classical Physics Quantum Physics 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. |
| title | Introduction to Higher Order Classical Dynamics: Pais-Uhlenbeck Model and Coupled Oscillators |
| topic | Physics Education High Energy Physics - Theory Mathematical Physics Classical Physics Quantum Physics |
| url | https://arxiv.org/abs/2605.20094 |