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Year 0·Month 6·Week 3

Day 160: Computational Lab — Hamiltonian Mechanics in Python

Day 160 of 2,016~17 min read

Learning Objectives

•Implement symbolic Poisson bracket calculations using SymPy
•Build phase space visualizers for arbitrary 2D Hamiltonian systems
•Implement symplectic integrators (Störmer-Verlet) and compare with non-symplectic methods
•Verify conservation laws numerically
•Visualize the transition from integrable to chaotic dynamics
•Create Poincaré sections to analyze higher-dimensional systems

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