First integrals versus configurational invariants and a weak form of complete integrability |
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| Authors: | W Sarlet PGL Leach F Cantrijn |
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| Institution: | Instituut voor Theoretische Mechanica, Rijksuniversiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium;Department of Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Johannesburg, 2001 South Africa;Instituut voor Theoretische Mechanica, Rijksuniversiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium |
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| Abstract: | A confusion over the concept of first integrals, which has been created in a recent paper by Hall 13] is clarified. The clear distinction between first integrals and functions which are first integrals only on a specific, fixed hypersurface is discussed. Hall's terminology of configurational invariants is adopted for the latter case. The possible relevance of knowing configurational invariants for a Hamiltonian system is illustrated by results concerning a weak form of the theory on complete integrability. |
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