This lesson covers the concept of stability analysis in mechanical models, focusing on single and two-degree of freedom systems. It explains the large deflection theory and the energy approach used in finding critical load and mode shape. The lesson also discusses the calculation of total potential energy in deformed configurations, considering both strain energy stored in springs and external work done. It provides detailed examples of stability models, explaining how to calculate the total potential energy, conditions for equilibrium, and the characteristic of equilibrium. The lesson concludes with the determination of mode shapes corresponding to different loads.

- Stability analysis in mechanical models involves understanding the large deflection theory and the energy approach.
- The total potential energy in deformed configurations is calculated considering the strain energy stored in springs and the external work done.
- The conditions for equilibrium involve the first variation of the total potential energy being equal to zero.
- The characteristic of equilibrium is determined by the second variation of the total potential energy.
- The mode shapes corresponding to different loads are determined by substituting the load values in the equilibrium equations.

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