Dissipative Perturbations of 3d Hamiltonian Systems
Fish, Daniel
arXiv, 0506047 / Harvested from arXiv
Text on arXiv
In this article we present some results concerning natural dissipative perturbations of 3d Hamiltonian systems. Given a Hamiltonian system dx/dt = PdH, and a Casimir function S, we construct a symmetric covariant tensor g, so that the modified (so-called 'metriplectic') system dx/dt = PdH + gdS satisfies the following conditions: dH is a null vector for g, and dS(gdS)< 0. Along solutions to a dynamical system of this type, the Hamiltonian function H is preserved while the function S decreases, i.e. S is dissipated by the system. We are motivated by the example of a relaxing rigid body by P.J. Morrison in which systems of this type were introduced.
Publié le : 2005-06-18
Classification:  Mathematical Physics,  53D17,  53B50,  70H09 
@article{0506047,
     author = {Fish, Daniel},
     title = {Dissipative Perturbations of 3d Hamiltonian Systems},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506047}
}

Fish, Daniel. Dissipative Perturbations of 3d Hamiltonian Systems. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506047/