A relativistic procedure for deriving the kinetic part of the generalized Euler equation is proposed as an argument to justify the application of the vortical equation of motion to the solution of classical discrete dynamics problems. An invariant formulation of the potential integration method for the vortical equation of motion is given for a definite class of two-dimensional motions. To demonstrate the efficiency of the method, a number of well-known theorems on the dynamics of a material point are proved. A new result of the study is the fact that zero-energy hyperelliptic motions are related to the field of ’multiplicative’ type forces.

PACS: 45.20.−d, 45.50.Pk (all) DOI: 10.1070/PU2002v045n11ABEH001171 URL: https://ufn.ru/en/articles/2002/11/c/ 000181345500003 Citation: Kukushkin A V "An invariant formulation of the potential integration method for the vortical equation of motion of a material point" Phys. Usp. 45 1153–1164 (2002) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Кукушкин А В «Инвариантная редакция потенциального метода интегрирования вихревого уравнения движения для материальной точки» УФН 172 1271–1282 (2002); DOI: 10.3367/UFNr.0172.200211c.1271