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 assumpt...
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| creator | Gorni, Gianluca Scomparin, Mattia Zampieri, Gaetano |
| 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. |
| doi_str_mv | 10.48550/arxiv.2104.14793 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.2104.14793</identifier><language>eng</language><subject>Mathematics - Dynamical Systems ; Mathematics - Mathematical Physics ; Physics - Mathematical Physics</subject><creationdate>2021-04</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2104.14793$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2104.14793$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Gorni, Gianluca</creatorcontrib><creatorcontrib>Scomparin, Mattia</creatorcontrib><creatorcontrib>Zampieri, Gaetano</creatorcontrib><title>Nonlocal constants of motion in Lagrangian Dynamics of any order</title><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
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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.</abstract><doi>10.48550/arxiv.2104.14793</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems Mathematics - Mathematical Physics Physics - Mathematical Physics |
| title | Nonlocal constants of motion in Lagrangian Dynamics of any order |
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