Bibliographic Details
| 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] |
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| Database: |
Education Research Complete |
