Nonlocal constants of motion in Lagrangian Dynamics of any order
We describe a recipe to generate “nonlocal” constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and estimates of solutions under fairly general assumptions. Then...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818122000031 |
| _version_ | 1811332115206242304 |
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| author | Gianluca Gorni Mattia Scomparin Gaetano Zampieri |
| author_facet | Gianluca Gorni Mattia Scomparin Gaetano Zampieri |
| author_sort | Gianluca Gorni |
| collection | DOAJ |
| description | We describe a recipe to generate “nonlocal” constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and estimates of solutions under fairly general assumptions. Then we review a generalization to Euler–Lagrange ODEs of order higher than two, leading to first integrals for the Pais–Uhlenbeck oscillator and other systems. Future developments may include adaptations of the theory to Euler–Lagrange PDEs. |
| first_indexed | 2024-04-13T16:31:59Z |
| format | Article |
| id | doaj.art-f233e470c7a1479ba40cce7bc08ff11f |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-13T16:31:59Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-f233e470c7a1479ba40cce7bc08ff11f2022-12-22T02:39:34ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812022-06-015100262Nonlocal constants of motion in Lagrangian Dynamics of any orderGianluca Gorni0Mattia Scomparin1Gaetano Zampieri2Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, via delle Scienze 208, 33100 Udine, ItalyVia del Grano 33, 31021 Mogliano Veneto, ItalyDipartimento di Informatica, Università di Verona, strada Le Grazie 15, 37134 Verona, Italy; Corresponding author.We describe a recipe to generate “nonlocal” constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and estimates of solutions under fairly general assumptions. Then we review a generalization to Euler–Lagrange ODEs of order higher than two, leading to first integrals for the Pais–Uhlenbeck oscillator and other systems. Future developments may include adaptations of the theory to Euler–Lagrange PDEs.http://www.sciencedirect.com/science/article/pii/S2666818122000031Higher-order LagrangiansNonlocal constantsFirst integralsDissipative mechanical systemsPais–Uhlenbeck oscillator |
| spellingShingle | Gianluca Gorni Mattia Scomparin Gaetano Zampieri Nonlocal constants of motion in Lagrangian Dynamics of any order Partial Differential Equations in Applied Mathematics Higher-order Lagrangians Nonlocal constants First integrals Dissipative mechanical systems Pais–Uhlenbeck oscillator |
| title | Nonlocal constants of motion in Lagrangian Dynamics of any order |
| title_full | Nonlocal constants of motion in Lagrangian Dynamics of any order |
| title_fullStr | Nonlocal constants of motion in Lagrangian Dynamics of any order |
| title_full_unstemmed | Nonlocal constants of motion in Lagrangian Dynamics of any order |
| title_short | Nonlocal constants of motion in Lagrangian Dynamics of any order |
| title_sort | nonlocal constants of motion in lagrangian dynamics of any order |
| topic | Higher-order Lagrangians Nonlocal constants First integrals Dissipative mechanical systems Pais–Uhlenbeck oscillator |
| url | http://www.sciencedirect.com/science/article/pii/S2666818122000031 |
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