In this paper we analyze in detail a collection of motivating examples to consider bm-
symplectic forms and folded-type symplectic structures. In particular, we provide models in
Celestial Mechanics for every bm-symplectic structure. At the end of the paper, we introduce
the odd-dimensional analogue to b-symplectic manifolds: b-contact manifolds.
Miranda, E., Delshams, A., Planas, A., Oms, C., Dempsey, R. "An invitation to singular symplectic geometry". 2017.