The Idea of a Lax Pair—Part I: Conserved Quantities for a Dynamical System.
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| Title: | The Idea of a Lax Pair—Part I: Conserved Quantities for a Dynamical System. |
|---|---|
| Authors: | Krishnaswami, Govind S.1 (AUTHOR) govind@cmi.ac.in, Vishnu, T. R.1 (AUTHOR) |
| Source: | Resonance: Journal of Science Education. Dec2020, Vol. 25 Issue 12, p1705-1720. 16p. |
| Subject Terms: | Conserved quantity, Dynamical systems, Equations of motion, Lax pair, Rigid bodies, Conservation laws (Mathematics), Curvature |
| Abstract: | Conserved quantities can help to understand and solve the equations of motion of various dynamical systems. Lax pairs are a useful tool to find conserved quantities of some dynamical systems. We give a motivated introduction to the idea of a Lax pair using examples such as the linear harmonic oscillator, Toda chain and Eulerian rigid body. A key step is to write the equations in 'Lax form', which makes it easy to read off conserved quantities. In Part II, these ideas will be extended from systems of particles to continuum systems of fields and also given a geometric interpretation in terms of curvature. [ABSTRACT FROM AUTHOR] |
| Copyright of Resonance: Journal of Science Education is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 147837956 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Idea of a Lax Pair—Part I: Conserved Quantities for a Dynamical System. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Krishnaswami%2C+Govind+S%2E%22">Krishnaswami, Govind S.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> govind@cmi.ac.in</i><br /><searchLink fieldCode="AR" term="%22Vishnu%2C+T%2E+R%2E%22">Vishnu, T. R.</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Resonance%3A+Journal+of+Science+Education%22">Resonance: Journal of Science Education</searchLink>. Dec2020, Vol. 25 Issue 12, p1705-1720. 16p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Conserved+quantity%22">Conserved quantity</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+motion%22">Equations of motion</searchLink><br /><searchLink fieldCode="DE" term="%22Lax+pair%22">Lax pair</searchLink><br /><searchLink fieldCode="DE" term="%22Rigid+bodies%22">Rigid bodies</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+laws+%28Mathematics%29%22">Conservation laws (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Curvature%22">Curvature</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Conserved quantities can help to understand and solve the equations of motion of various dynamical systems. Lax pairs are a useful tool to find conserved quantities of some dynamical systems. We give a motivated introduction to the idea of a Lax pair using examples such as the linear harmonic oscillator, Toda chain and Eulerian rigid body. A key step is to write the equations in 'Lax form', which makes it easy to read off conserved quantities. In Part II, these ideas will be extended from systems of particles to continuum systems of fields and also given a geometric interpretation in terms of curvature. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Resonance: Journal of Science Education is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s12045-020-1091-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1705 Subjects: – SubjectFull: Conserved quantity Type: general – SubjectFull: Dynamical systems Type: general – SubjectFull: Equations of motion Type: general – SubjectFull: Lax pair Type: general – SubjectFull: Rigid bodies Type: general – SubjectFull: Conservation laws (Mathematics) Type: general – SubjectFull: Curvature Type: general Titles: – TitleFull: The Idea of a Lax Pair—Part I: Conserved Quantities for a Dynamical System. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Krishnaswami, Govind S. – PersonEntity: Name: NameFull: Vishnu, T. R. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 09718044 Numbering: – Type: volume Value: 25 – Type: issue Value: 12 Titles: – TitleFull: Resonance: Journal of Science Education Type: main |
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