Geodesic structure of naked singularities in 
AdS3
 spacetime
We present a detailed study of the geodesics around naked singularities in AdS$_3$. These spacetimes are obtained through identifications along spacelike Killing vectors with a fixed point, and are in general interpreted as massive spinning point particles. The general solution to the geodesic equation is expressed in terms of elementary functions. We classify different geodesics in terms of their radial bounds, which depend on the constants of motion. Null geodesics always escape to infinity and can reach the singularity for some values of these constants. Timelike geodesics never escape to infinity and do not always fall into the singularity. The spatial projections of the geodesics (polar orbits) exhibit self-intersections, which are particularly simple for null geodesics. As a particular application, we also compute the lengths of fixed-time spacelike geodesics of the static naked singularity using two different regularizations.