Lagrangian-Based Dynamic Modeling & Simulation of a Double Spring Pendulum in MATLAB

🎯 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