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-# Lagrange multiplier method project
-This is a project I did with two of my friends for the course Dynamics of Mechanical Systems.
-In this experiment, we studied the motion of a ball placed on a wire shaped like a parabola which rotates around its axis of symmetry with a constant angular velocity.
-The goal of the experiment is to derive the equations of motion using the Lagrange multiplier method for solving constrained optimization problems, represent them as a system of differential equations via the Constraint Stabilization method, and then analyze graphs of relevant quantities.
-We completed the project in Python using Numpy, Matplotlib and SciPy libraries.
+# Motion of a Ball on a Rotating Parabolic Wire: Lagrange Multiplier Method
+
+This project explores the dynamics of a ball placed on a wire shaped like a parabola, which rotates around its axis of symmetry at a constant angular velocity. The aim was to derive the equations of motion using the Lagrange multiplier method for constrained systems, reformulate them as a system of differential equations using the Constraint Stabilization method, and analyze the motion through visualizations of key quantities.
+
+# Key Libraries:
+**NumPy:** Utilized for numerical calculations, particularly in solving systems of differential equations, handling matrices, and performing vectorized operations for efficient computation.
+
+**SciPy:** Applied for solving the system of differential equations derived from the Lagrangian, using robust numerical solvers.
+
+**Matplotlib:** Employed for generating and analyzing graphs that represent the ball's motion, velocities, and other relevant physical quantities.
+
+# Key Features:
+
+_**Lagrange Multiplier Method:** _This method is used to derive the equations of motion for a system under constraints, forming the core of the project.
+
+_**Constraint Stabilization:**_ The system of equations is transformed using this method to stabilize the constraints and ensure physically meaningful solutions.
+
+_**Numerical Simulation and Visualization:**_ Python libraries are combined to simulate the motion and visualize the results, providing insights into the behavior of the system over time.
+
+# Project Context:
+This project was completed as part of the course Dynamics of Mechanical Systems and was a collaboration with two other students. It serves as a practical application of theoretical concepts to model and simulate real-world mechanical systems.