Ricci soliton equation with application to a coupled pendula


  • Marius Ionescu Institute of Solid Mechanics of the Romanian Academy
  • Ligia Munteanu Institute of Solid Mechanics of the Romanian Academy
  • Veturia Chiroiu Institute of Solid Mechanics of the Romanian Academy
  • Valerica Mosnegutu Institute of Solid Mechanics of the Romanian Academy
  • Dan Dumitriu Institute of Solid Mechanics of the Romanian Academy
  • Iulian Grip Institute of Solid Mechanics of the Romanian Academy


Ricci soliton, pendulum, cnoidal theory


The Ricci equation and the soliton solutions are obtained in this paper for two coupled pendula in order to optimise its locomotion and structure. The robot is swinging repeatedly like a rope with successive movement steps along a mobile support. The cnoidal theory and a genetic algorithm are used to solve the problem via the Ricci solitons and the pseudospherical reduction of the rheological Zener equations. The Bäcklund transform is applied to Ricci equation to generate pseudo-spherical surfaces.


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