Potential-density pairs for bent bars
  A method is presented to bend a thin massive line when the curvature is
small. The procedure is applied to a homogeneous thin bar with two types of
curvatures. One of them mimics a galactic bar with two spiral arms at its tips.
It is showed that if the bending function is a linear combination of Legendre
polynomials, then the bent potential is an exact solution of the Laplace
equation. A transformation is applied on the thin bent bars to generate
three-dimensional potential-density pairs without singularities. The potentials
of the thin bent bars are also used to generate non-axisymmetric planar
distributions of matter.
