classical-mechanics

What I do

• Apply Newton's laws to particle and rigid body motion
• Solve problems using Lagrangian and Hamiltonian mechanics
• Analyze central force motion and orbital dynamics
• Calculate small oscillations and normal modes
• Study chaotic systems and sensitivity to initial conditions
• Model collisions and conservation of momentum/energy

When to use me

When analyzing mechanical systems, designing machinery, or studying planetary/celestial motion.

Key Concepts

• Newton's Second Law: F = ma relates force to acceleration
• Lagrangian: L = T - V, action S = ∫L dt, principle of least action
• Hamiltonian: H = T + V, canonical equations ∂q_i/∂t = ∂H/∂p_i
• Conservation Laws: Energy, momentum, angular momentum from symmetries
• Central Forces: Effective potential enables reduction to 1D problem
• Rigid Body: Angular momentum L = I·ω, Euler's equations