Motions of a swinging Atwood's machine

N. Tufillaro

The Lagrangian Lμ (r, θ) = 1/2(1 + μ)r2 + 1 2r2 θ2- r(μ - cos θ) with 1 < μ ≤ 3.1 is studied using a surface of section map. Regular and chaotic behaviour is exhibited. The numerical evidence suggests the motion is integrable for μ = 3. Integrability is proved by explicitly exhibiting a first integral.

Mots clés: chaos; dynamics

Domaines: Articles anciens

N. Tufillaro. Motions of a swinging Atwood's machine. Journal de Physique, 1985, 46 (9), pp.1495-1500. ⟨10.1051/jphys:019850046090149500⟩. ⟨jpa-00210094⟩