Individual skill
hamiltonian-mechanics
Hamiltonian mechanics — symplectic integrators (leapfrog, Yoshida), Hamilton's equations, Poisson brackets, canonical transformations, action-angle variables, and KAM theory analysis. Use for energy-conserving long-time integration of conservative systems.
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# Hamiltonian Mechanics
## Overview
Solve Hamilton's equations using symplectic integrators that exactly conserve the symplectic structure and approximately conserve energy for exponentially long times. Essential for N-body problems, celestial mechanics, molecular dynamics, and any conservative system needing long-time accuracy.
## When to Use
- Conservative (energy-preserving) systems
- Long-time integration (thousands of orbits, molecular dynamics)
- N-body gravitational or Coulomb problems
- When energy drift from standard RK45 is unacceptable
- Phase space structure analysis (KAM tori, resonances)
