Curves in the Lorentz-Minkowski plane with curvature depending on their position Castro Infantes, Ildefonso Castro Infantes, Jesús Lorentzian curves Curvature Singer’s problem Sinusoidal spirals Elastic curves Grim-reaper curves Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in the Lorentz-Minkowski plane, focusing on spacelike and timelike curves. In this article, we study those curves in 2 whose curvature depends on the Lorentzian pseudodistance from the origin, and those ones whose curvature depends on the Lorentzian pseudodistance through the horizontal or vertical geodesic to a fixed lightlike geodesic. Making use of the notions of geometric angular momentum (with respect to the origin) and geometric linear momentum (with respect to the fixed lightlike geodesic), respectively, we get two abstract integrability results to determine such curves through quadratures. In this way, we find out several new families of Lorentzian spiral, special elastic and grim-reaper curves whose intrinsic equations are expressed in terms of elementary functions. In addition, we provide uniqueness results for the generatrix curve of the Enneper surface of second kind and for Lorentzian versions of some well-known curves in the Euclidean setting, like the Bernoulli lemniscate, the cardioid, the sinusoidal spirals and some nondegenerate conics. We are able to get arc-length parametrizations of them and they are depicted graphically. 2020-10-05T12:54:41Z 2020-10-05T12:54:41Z 2020-07 info:eu-repo/semantics/article Castro, I., Castro-Infantes, I., & Castro-Infantes, J. (2020). Curves in the Lorentz-Minkowski plane with curvature depending on their position. Open Mathematics, 18(1), 749-770. [https://doi.org/10.1515/math-2020-0043] http://hdl.handle.net/10481/63673 10.1515/math-2020-0043 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España DE GRUYTER POLAND SP Z O O, BOGUMILA ZUGA 32A STR, 01-811 WARSAW, MAZOVIA, POLAND