Newtonian Mechanics

The floor plan of physics. Every other group renovates from here.

• Group — newtonian-mechanics
• Operators — 13 (NM18 – NM30)
• Anchor operators — KO42 · NM19 · NM26 · NM30
• Verification — energy and momentum conservation under error_pct ≤ 0.1%; oscillators land within 1 ms of Zeqond grid

What it unifies

The 13 Newtonian operators cover the classical foundations every engineer uses daily: three laws of motion, gravity, work-energy, conservation of momentum, angular kinematics, and the harmonic oscillator. In Zeq they are not legacy code — they are the deterministic kernel lane that all other groups plug into when they need a classical fallback.

F = ma (NM19) is the most-called operator on the network. Pair it with KO42 and every simulated force is Zeqond-phase sealed, so long-horizon integration stays stable. The harmonic oscillator (NM30) is the canonical bridge into HulyaPulse — its ω is naturally scalable to 2π · 1.287 Hz whenever you need to tether a classical system to the kernel clock.

Operator catalog

ID	Formula	Role
NM18	∑F = 0 ⇒ v = const	First law (inertia)
NM19	F = ma	Second law
NM20	F₁₂ = −F₂₁	Third law (reaction)
NM21	F = G m₁ m₂ / r²	Universal gravitation
NM22	W = F·d	Work
NM23	KE = ½ mv²	Kinetic energy
NM24	PE = mgh	Gravitational potential energy
NM25	KE + PE = const	Energy conservation
NM26	p = mv	Linear momentum
NM27	∑p_init = ∑p_final	Momentum conservation
NM28	L = r × p	Angular momentum
NM29	τ = r × F	Torque
NM30	F = −kx , x(t) = A cos(ωt + φ)	Harmonic oscillator

Runnable worked example — 1 kHz spring tethered to HulyaPulse

curl -X POST https://api.zeq.dev/api/playground/compute \
  -H "Authorization: Bearer demo-key" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["KO42", "NM30", "NM25"],
    "inputs": {
      "mass_kg": 0.287,
      "k_N_per_m": 11326.5,
      "amplitude_m": 0.02,
      "duration_s": 0.777
    }
  }'

Expected response shape:

{
  "ok": true,
  "phase": 0.638,
  "zeqond": 1798346638.1,
  "result": {
    "omega_rad_s": 198.63,
    "energy_conserved_pct": 99.942,
    "phase_drift_vs_hulyapulse": 0.0008,
    "error_pct": 0.058
  }
}

Extend it

1. Rigid body — chain NM28 + NM29 for gyroscopic stabilization with Zeqond-locked torque scheduling.
2. Orbital — pair NM19 + NM21 for multi-body orbital propagation with ≤0.1% drift across hours of integration.
3. Collisions — NM26 + NM27 for inelastic collision chains that respect mesh-level conservation receipts.

Seeds

• Near — a Zeq-native physics engine for game/robotics teams with drop-in replacement of Box2D/Bullet solvers.
• Medium — PhaseLock Motors — control loops that target HulyaPulse phase instead of simple PID setpoints.
• Far — a kinematics workbench where classical + relativistic + quantum regimes compose into one field, no glue code.

Papers

• Zeq paper — https://doi.org/10.5281/zenodo.18158152
• Framework paper — https://doi.org/10.5281/zenodo.15825138

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.