ffsshhttiikk 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