Effect of Initial Perturbations on Stability of Autonomous Bicycle—A Graphical Approach

Abstract The present article attempts to perform a quasi-dynamic analysis of bicycle stability from the viewpoint of initial perturbations and understand the stable and unstable behaviors. Like earlier researchers, the bicycle is idealized as four interconnected bodies—the front wheel, the front fork, the main body, and the rear wheel joined by revolute joints. The forces on the bicycle are limited to their weights, centrifugal forces, and gyroscopic moments. The two primary degrees-of-freedom analyzed are the bicycle lean (tilt) angle and the steering angle of the front wheel. A systematic matlab simulation analysis illustrates the results through trajectories, phase plots, and moment contours. This graphical approach helps to identify the effect of small but finite initial perturbations on the stability, offering intuitive insights into the nonlinear dynamics governing self-stability.