Stability of Mechanical Systems

This lecture covers the concept of virtual work in determining equilibrium positions of mechanical systems, focusing on stability analysis. Through examples of pin-connectors and rigid systems, the instructor explains how to calculate support reactions using the principle of virtual work. The lecture delves into the types of stability, conservative forces, and the criterion for determining stable, neutral, and unstable equilibrium positions. It also explores the potential energy and the significance of higher derivatives in evaluating stability. The instructor demonstrates the evaluation of equilibrium positions and stability through mathematical derivations and practical examples.