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.
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.
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.
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.