Explore the intricacies of projectile motion through the lens of Hamiltonian mechanics and polar coordinates in this 26-minute video tutorial. Delve into a unique approach to solving projectile motion problems, combining advanced mathematical concepts with practical applications. Gain insights into the "why" behind using Hamiltonian mechanics for this classic physics problem, and follow along with the provided Python code to visualize and understand the solution. Enhance your understanding of physics and mathematical modeling while discovering the elegance of solving complex problems using alternative coordinate systems.