Potential-density pairs for bent bars

Abstract

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.