Numerical methods are usually necessary in solving Hamiltonian systems since there is often no closed-form solution. By utilizing a general property of Hamiltonians, namely the symplectic property, all of the qualities of the system may be preserved for indefinitely long integration times because all of the integral (Poincare) invariants are conserved. This allows for more reliable results and frequently leads to significantly shorter execution times as compared to conventional methods. The resonant triad Hamiltonian with one degree of freedom will be focused upon for most of the numerical tests because of its difficult nature and, moreover, analytical results exist whereby useful comparisons can be made.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc278485 |
| Date | 05 1900 |
| Creators | Curry, David M. (David Mason) |
| Contributors | Renka, Robert Joseph, Neuberger, J. W. (John W.), 1934-, Jacob, Roy Thomas |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | vi, 51 leaves : ill., Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Curry, David M. (David Mason) |
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