This lesson covers the concept of numerical methods for non-linear system analysis. It delves into how to solve a set of non-linear equations and numerical solutions for ODE and DD equations. The lesson also explores the Poincare section, FFT, and Lyapunov exponents. It further discusses different types of chaos and how to identify chaotic systems. The lesson also explains the use of symbolic software to develop equations of motion and the application of numerical differentiation and integration. It also touches on the use of various methods like the finite difference method, Runge Kutta method, Wilson Theta method, and Newmarket method to solve differential equations.

- Rigid structures are often bulky, heavy, and require large amounts of energy to operate, making them less efficient.
- The mathematical modeling of flexible structures is complex due to their low stiffness and susceptibility to vibrations.
- The vibration problem in flexible structures can be solved by improving their dynamic models and incorporating different control strategies.

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