The following table considers quadratic Hamiltonians
to have a 4th degree first integral. Equations of motion
are formulated using a Poisson bracket that is related to the Lie
algebra e(3). Three variations are discussed in:
T. Wolf, O.V. Efimovskaya: Classification of integrable
quadratic Hamiltonians on e(3), Regular and Chaotic Dynamics,
8, no 2 (2003), p 155-162, (or the preprint
nlin.SI/0302001).
Computations reported in the table were performed with the computer algebra system REDUCE running with 120 MB under Linux on a 1.7 GHz Pentium 4 PC.
Quadratic Hamiltonians with a Poisson structure related to the Lie algebra e(3)
| problem type | e(3) | e(3), J_2=0 | e(3) quantum |
| # of unknowns in the Hamiltonian | 17 | 17 | 17 |
| # of unknowns in the first integral | 200 | 176 | 200 |
| total # of unknowns | 217 | 193 | 217 |
| # of conditions | 451 | 396 | 451 |
| total # of terms in all conditions | 5469 | 5243 | 9681 |
| average # of terms in a condition | 12.1 | 13.2 | 21.5 |
| time to solve conditions | 18h 53min | approx 15h | 11h 43min |
| # of solutions | 6 | 6 | 6 |
This page is maintained by
Thomas Wolf