This lesson covers the principles of non-linear vibration, focusing on the derivation of the equation of motion. It builds on the previous two lessons, where Newton's second law or D'alembert principle was used to derive the equation for discrete and distributed mass systems. The lesson also introduces the use of the LaGrange principle in deriving the equation of motion. For instance, the LaGrange principle can be used to derive the equation of motion for a pendulum, a common example of a non-linear vibration system.

- The extended Hamilton principle is used when there are non-conservative forces acting on the system, and includes the work done due to these forces.
- The equation of motion can be derived using the Hamilton's principle when there are no non-conservative forces acting on the system.
- The spacio temporal equation of motion can be derived using the D'alembert principle.

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