Physics - Advanced Classical Mechanics - Hamiltonian mechanics - Hamiltonian Problems

5 problems. P1: 'Harmonic oscillator: L = ½mq̇² - ½kq². Momentum p = ∂L/∂q̇ = ___' (mq̇). P2: 'H = pq̇ - L = p(p/m) - ½m(p/m)² + ½kq² = ___' (p²/(2m) + ½kq²). P3: 'Hamilton's equations: q̇ = ∂H/∂p = ___' (p/m). P4: 'ṗ = -∂H/∂q = ___' (-kq). P5: 'Combining: q̈ = ṗ/m = -kq/m → SHM with ω = ___' (√(k/m

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Physics - Advanced Classical Mechanics - Hamiltonian mechanics - Hamiltonian Problems
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Physics - Advanced Classical Mechanics - Hamiltonian mechanics - Hamiltonian Problems

vivmagarwal
vivmagarwalJan 29, 2026

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5 problems. P1: 'Harmonic oscillator: L = ½mq̇² - ½kq². Momentum p = ∂L/∂q̇ = ___' (mq̇). P2: 'H = pq̇ - L = p(p/m) - ½m(p/m)² + ½kq² = ___' (p²/(2m) + ½kq²). P3: 'Hamilton's equations: q̇ = ∂H/∂p = ___' (p/m). P4: 'ṗ = -∂H/∂q = ___' (-kq). P5: 'Combining: q̈ = ṗ/m = -kq/m → SHM with ω = ___' (√(k/m

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PhysicsAdvanced Classical MechanicsUndergraduate, Undergraduate, Undergraduate, Undergraduate Advanced, Undergraduate

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