A Dual Lagrange Multiplier Approach for the Dynamics of the Mechanical Systems

Abstract

The variational iteration method, a powerful tool for solving nonlinear oscillators with initial conditions, has been expanded to accommodate two-point boundary conditions. In this modification, two Lagrange multipliers are introduced, and their identification process mirrors that of the conventional approach. A generalized equation is provided for a category of highly nonlinear mechanical systems, followed by three illustrative examples derived from this generalized equation. These examples serve to demonstrate the effectiveness of the method. The solutions produced by this modified approach not only show remarkable agreement with numerical results but also exhibit superior accuracy when compared to outcomes obtained through other established methods.

Keywords

• amplitude-frequency relationship
• lagrange multiplier
• variational principle
• nonlinear conservative oscillator