Spherical generalized helices in 3-dimensional Lorentz-Minkowski space

In this paper we analyze generalized helices lying on the non-degenerated quadric surfaces in 3-dimensional Lorentz-Minkowski space, i.e. on a pseudosphere and in a hyperbolic plane. We provide their characterizations in terms of curvature and torsion and analyze their projections onto planes orthogonal to their axes. We show that these projections appear as Euclidean or Lorentzian cycloidal curves, so we also introduce natural equations and parametrizations of Lorentzian cycloidal curves.