quantumquirkxyz Contract
- Input: problem description and inputs defined by the skill body.
- Output: Markdown artifact with completed process steps.
- Side effects: none.
- Dependencies: none.
- Stop condition: all process steps executed; artifact saved with required sections.
- Risk: low.
- Boundary: produces reasoning artifact only; no system changes.
Classical Mechanics
Solve a classical mechanics problem — Newton's laws, Lagrangian, Hamiltonian, or orbital — with free-body analysis, energy accounting, and dimensional checks.
When to use
- A mechanical system needs its motion solved (forces, trajectories, equilibrium).
- Engineering, robotics, aerospace, or sports analysis.
- Rigid body rotation, orbital mechanics, or vibrations.
Process
- Identify system — particles, rigid body, continuous; degrees of freedom.
- Draw free-body diagram — all forces with direction, labels, and units.
- Choose formulation — Newtonian (F=ma), Lagrangian (L=T−V), Hamiltonian (H=T+V), or energy methods.
- Write equations — Newton's 2nd / Euler-Lagrange / Hamilton's equations; include constraints (holonomic / nonholonomic).
- Solve — analytically (harmonic oscillator, projectile, central force) or numerically (RK4 for ODEs, finite elements).
- Dimensional check — verify [force]=[mass][acceleration]; no hidden unit mismatches.
- Physical limits — check limiting cases (small angle, large mass, friction → 0).
- Deliver — artifact: diagram, formulation, equations, solution, dimensional check, and limiting cases.