Stability of Equilibrium Points in the Double Planar Pendulum System: An Algebraic Approach

This work presents the derivation of equations of motion for the double planar pendulum system. An in-depth examination of equilibrium point stability then followed by use of the Lyapunov-Poincar Linearization Theorem and the Hurwitz Criterion. These tools are used for the linearized system to examine equilibrium configuration stability, presenting an algebraic approach and detailed examination of the dynamic behavior of the system.