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.Comment: 14 pages, 1 figur