Application of Lagrange equations to 2D double spring-pendulum in generalized coordinates

Abstract

In this study, the Lagrange’s equations of motion for a 2D double spring-pendulum with a time dependent spring extension have been derived and solved approximately. The resulting equations are also solved numerically using Maple, and plots of motion for the pendulum bobs m1 and m2 are presented and compared. It was observed that motion along the x-axis is characterized by sine wave function while motion along y-axis is characterized by cosine wave function with slightly changing amplitudes. Change in stiffness constant, angle of deflection, mass of pendulum bob and spring length were found to have significant effect on the dynamics of the double spring-pendulum. The periodic and chaotic behaviour noticed in this study is consistent with current literature on spring-pendulum systems.

Keywords

• lagrange equations
• double spring-pendulum