Motion with friction of a heavy particle on a manifold - applications to optimization
Alexandre Cabot (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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Let Φ : be a function on a real Hilbert space and ∑ ⊂ the manifold defined by ∑ := Graph (Φ). We study the motion of a material point with unit mass, subjected to stay on and which moves under the action of the gravity force (characterized by ), the reaction force and the friction force ( is the friction parameter). For any initial conditions at time , we prove the existence of a trajectory defined on . We are then interested in the asymptotic...