Extended Hamilton's Principle — Lesson 2

This lesson covers the principles of non-linear vibration, focusing on the derivation of non-linear equations of motion. It delves into the lumped parameter model and the distributed mass model, two approaches introduced in the previous class. The lesson further explains the force and moment-based approach, utilizing Newton's second law and D'alembert's principle. The application of these principles to distributed mass systems, also known as continuous systems, is discussed in detail.

Video Highlights

06:00 - Equations for a continuous system - Euler Bernoulli Beam
27:43 - Equations for a continuous system - beam with vertical motion
51:22 - Lagrange principle - Energy-based approach

Key Takeaways

- The force and movement-based approach utilizes Newton's second law and D'albert principle.
- The equation of motion of a simple spring mass system can be derived using the Newton's second law or the D'alembert principle.
- The continuous systems, such as the Euler Bernoulli beam, require partial differential equations to describe their motion.