Hamilton's Principles for Formulating Vibration Problems — Lesson 3

This lesson covers the method of formulating vibration problems using Hamilton's principle. It discusses the derivation of Hamilton's principle and its application in deriving the equation of motion for dynamic systems. The lesson also explains how to use Hamilton's principle to formulate vibration problems in continuous systems, providing an example of a bar undergoing axial vibration. It further discusses the concept of Newtonian and varied paths in virtual displacement fields. The lesson concludes with the application of Hamilton's principle in systems with non-conservative force fields.

Video Highlights

01:30 - Introduction to Hamilton's Principle.
02:39 - Application of Hamilton's Principle.
05:25 - Explanation of Newtonian and Varied Path.
43:18 - Application of Hamilton's Principle to a Two Degree Freedom System.

Key Takeaways

- Hamilton's principle is a technique used to formulate vibration problems, especially in continuous systems.
- The principle utilizes energy expressions and is based on the integration of the variation of total energy.
- Hamilton's principle can derive the governing differential equation of motion and boundary conditions simultaneously.
- The principle is applicable when the energy of the system is clearly known.
- The principle can be modified to consider non-conservative force fields in the formulation of problems.