Integrability and non-integrability in Hamiltonian mechanics

V. Kozlov (1)

1 SMI | RAS - Steklov Mathematical Institute [Moscow]

In 1834, Hamilton expressed the differential equations of classical mechanics, the Lagrange equations $$\frac{d}{dt} \frac{\partial L}{\partial \dot{q}} = \frac{\partial L}{\partial q}$$ with $L:\mathbb{R}^n\times \mathbb R ^n \to \mathbb R$ in the "canonical form": $$\dot{q}=\frac{\partial H}{\partial p},\quad \dot{p}=- \frac{\partial H}{\partial q}$$ Here $p = \partial L/\partial \dot{q} \in \mathbb R^n$ is the generalized momentum and the Hamiltonian function $H= p\dot{q}- L\big|_{p,q}$ is the "total energy" of the mechanical system.

Mots clés: Hamiltonian system

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

V. Kozlov. Integrability and non-integrability in Hamiltonian mechanics. Russian Mathematical Surveys, 1983, 38 (1), pp.1-76. ⟨10.1070/RM1983v038n01ABEH003330⟩. ⟨hal-01349791⟩