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The paper aims to introduce some partial differential equations on Twistorial generalized K¨ ahler manifolds, with an emphasis on Euler-Lagrange equations. Twistor spaces are certain complex 3-manifolds which are associated with special conformal Riemannian geometries on 4-manifolds. Also, classical mechanic is one of the major subfields for mechanics system. A mechanical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space. Euler-Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. In this study, showing motion modeling partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the Maple software. Additionally, of the implicit solution of the equations to be drawn the graph.

Euler-Lagrange equations for holomorphic structures on twistorial generalized Kähler manifolds