Non-linear Dynamical Analysis of an Inverted Pendulum Cart Mechanism using Bifurcation Method

摘要

This paper presents the innate behavior of an Inverted Pendulum, which is an iconic symbol for nonlinear, unstable, underactuated, non-minimum-phase, non-holonomic multi-variable, fourth order system, etc. These characters, exhibited by the model plays a vital role in various fields of Engineering and Science. What makes them interesting is the Topological properties owned by the equilibrium points, in an Inverted Pendulum. The rigorous investment of Topology via techniques from Bifurcation Theory is presented here. This helps, one to gain intuition about the behavior of complex dynamical systems, from a quantum level to macroscopic systems.