Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion
The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on (3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S associated to the dynamics...