HAMILTONIAN SYSTEM
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1506 ▶ |
| Object type | Methodology or model |
A system whose study is amenable to Hamiltonian mechanics.
Hamiltonian systems are governed by Hamiltonian dynamics i.e. in R. THOM's words “A dynamics where there is no energy lost through dissipation” and as a result “the look of trajectories is not notably modified” (1993, p.41).
M. FARGE writes: “Hamiltonian mechanics deals only with stable states, or close to equilibrium, and describes only conservative, i.e. reversible phenomena, while turbulent flows are highly unstable and dissipative, i.e. irreversible; moreover classical dynamics always started from systems with few interactive elements, without a great number of degrees of freedom” (1992, p.212).
Only homeostatic systems are amenable to Hamiltonian mechanics, because in G. NICOLIS words they: “admit a variety of conservation laws, constraining their evolution very strictly”. But “as a counterpart they present rather poor stability properties in the sense that their evolution remains strongly dependent on the initial conditions” (1981, p.188). In other words, they are tightly deterministic. Dissipative, bifurcative systems are unstable and non-Hamiltonian. Note the correlation with POINCAR-'s 3-bodies or n-bodies problem.
Now that deterministic chaos and dissipative structuration have been discovered and researched, it becomes obvious that Hamiltonian systems and dynamics are rather abstract and theoretic models of not so common systems or very simplified ones.