弯曲杆的势-密度对
Potential-density pairs for bent bars
摘要：
提出了一种在曲率较小时弯曲细长直线的方法。该程序适用于一个均匀的薄杆两种类型的曲率。其中一个模拟了一个顶端有两个旋臂的银河棒。证明了如果弯曲函数是勒让德多项式的线性组合，则弯曲势是拉普拉斯方程的精确解。一个变换应用于薄弯曲杆产生三维的潜力，密度对没有奇异性。薄弯曲杆的潜力也被用来产生非轴对称的平面分布的物质。
英文摘要：
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.
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