Hamiltonian: Particle on a Frictionless Cylinder with a Force

Explore a detailed physics problem solving session focused on Hamiltonian mechanics. Dive into the analysis of a particle's motion on a frictionless cylinder under the influence of an external force. Follow along as the instructor breaks down problem 13 from chapter 13 of Taylor's Classical Mechanics textbook. Learn how to write and solve Hamilton's equations for this specific scenario, involving a mass m constrained to a cylinder of radius R and subjected to a force F = -kr. Gain insights into the application of cylindrical coordinates and the treatment of frictionless surfaces in mechanical systems. Enhance your understanding of Hamiltonian formalism and its practical use in describing particle motion. Complement your learning with a provided Python code implementation, allowing you to visualize and further explore the problem's solution.