Algebraic linearization criteria for systems of ordinary differential equations
The authors give all possible algebras of dimension 4 connected with the linearization by general point transformation for a system of two second-order ODEs. These results complement and complete the work [\textit{C. W. Soh} and \textit{F. M. Mahomed}, Int. J. Non-Linear Mech. 36, No. 4, 671--677 (2001; Zbl 1345.34012)]. Complete algebraic linearization criteria for dimension four algebras are provided. Necessary and sufficient conditions for linearization via invertible maps of a nonlinear to a linear system are given. To illustrate the obtained results, examples from Newtonian mechanics are presented.
scientific article; zbMATH DE number 6057929
scientific article