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Quantum Engineering Year 0: Mathematical Foundations Month 6Day 156

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Year 0·Month 6·Week 3

Day 156: Hamilton's Equations of Motion

Day 156 of 2,016~10 min read

Learning Objectives

•Derive Hamilton's equations from the Legendre transform
•Derive Hamilton's equations from Hamilton's principle
•Solve Hamilton's equations for standard systems
•Understand the first-order structure of Hamiltonian dynamics
•Recognize cyclic coordinates and conservation laws
•Compare Lagrangian and Hamiltonian formulations

Today's Schedule (7 hours)

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1 Derivation from the Legendre Transform 2 Derivation from Hamiltons Principle 3 Structure of Hamiltons Equations 4 Conservation of the Hamiltonian 5 Cyclic Coordinates and Conservation 6 Comparison Lagrangian vs Hamiltonian 7 Quantum Mechanics Connection

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