Solving Nonlinear Second-Order ODEs via the Eisenhart Lift and Linearization

Abstract

The linearization of nonlinear differential equations represents a robust approach to solution derivation, typically achieved through Lie symmetry analysis. This study adopts a geometric methodology grounded in the Eisenhart lift, revealing transformative techniques that linearize a set of second-order ordinary differential equations. The research underscores the effectiveness of this geometric approach in the linearization of a class of Newtonian systems that cannot be linearized through symmetry analysis.

Keywords

• linearization
• second-order ODEs
• Hamiltonian systems
• Newtonian physics