ABSTRACT

In this paper, the Lagrangian and equations of motion of a system consisting of four body particles coupled by three springs are determined. Numerous disciplines, including physics, engineering, and applied mathematics, are very interested in the dynamic behavior of such systems. We hope to gain an in-depth understanding of the system's behavior and its consequences for mechanical dynamics by applying the concepts of Lagrangian mechanics. First, we use the concept of least action to derive the Lagrangian function for the system, establishing a theoretical foundation. In order to do this, generalized coordinates must be defined, kinetic and potential energies must be computed, and the Lagrangian must be expressed as a function of these coordinates and their immediate derivative. From there, we apply the Euler-Lagrange equation to obtain the equations of motion controlling the system's time dynamics. We were able to obtain the accurate equation of motion for each mass by following these procedures.