🎯 Analyze Nonlinear Dynamics Using Energy-Based Modeling

This project presents a complete Lagrangian formulation and MATLAB simulation of a Double Spring Pendulum system, capturing its highly nonlinear and coupled dynamics. It is ideal for understanding advanced concepts in classical mechanics, vibrations, and control systems through a practical, simulation-based approach.

The model derives equations of motion using energy methods and solves them numerically to visualize system behavior under different initial conditions and parameters.

⚙️ Key Features

✅ Full Lagrangian dynamic derivation
✅ Nonlinear coupled equations of motion
✅ MATLAB implementation with ODE solvers
✅ Time-domain response plots (angles, velocities)
✅ Energy analysis & phase portraits
✅ Configurable masses, lengths & spring constants
✅ Clean, well-commented MATLAB code
✅ Ready for academic reports & demos

📦 What’s Included

📁 MATLAB source codes & functions
📄 Detailed PDF explaining theory & derivation
📊 Simulation scripts with plotting routines
📝 Example initial conditions & test cases
📈 Result visualization (time histories & phase plots)

🎓 Applications

• Classical & analytical mechanics courses

• Vibrations and dynamic systems study

• Control system modeling practice

• Nonlinear dynamics & chaos analysis

• Final year / semester projects

• MATLAB learning for mechanical engineers

💻 Requirements

• MATLAB (any recent version)

• Basic knowledge of dynamics & ODEs

🌟 Why Choose This Project?

✔️ Clear step-by-step Lagrangian formulation
✔️ Perfect bridge between theory & simulation
✔️ Highly customizable parameters
✔️ Saves time on derivations & coding
✔️ Professional structure for submission