Hamilton Equations of Pendulum-Spring System

Abstract. The pendulum-spring system was studied by using Hamilton equations of motion. The total Hamiltonian of this system is complicated because of the complex mechanical system. The paper begins by introducing the physical system and defining a fixed coordinate system. Following this, the Lagrangian and Hamilton equations of motion are derived. Six equations of motion are obtained from the Hamilton equations in the form of ordinary differential equation. These equations can be employed for simulating the dynamical behavior of the system. The primary goal of this paper is to familiarize physics students with the Hamilton equations of motion as applied to the pendulum-spring system.Keywords: Hamiltonian, pendulum, equation of motion, OD