Mechanical Hamiltonization of unreduced φ-simple Chaplygin systems - Anahory, Alexandre; Marrero, Juan Carlos; Martín de Diego, David (Wiley, 2025)
In this paper, we prove that the trajectories of unreduced 𝜙-simple Chaplygin kinetic systems are reparameterizations of horizontalgeodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannian metrics, which are not unique, are obtained explicitly in interesting examples. We also extend these results to 𝜙-simple Chaplygin mechanical systems (not necessarily kinetic).
Keywords: 12 Matemáticas; ODS 9 - Industria, innovación e infraestructura; Hamiltonization; unreduced systems; φ-simple Chaplygin systems; Riemannian submersions.