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 — `F = ma`, sealed to HulyaPulse

A synchronized computation: KO42 (the 1.287 Hz metric tensioner) composed with NM19 (F = ma). KO42 phase-locks the result to the kernel clock, so the force comes back stamped to the exact Zeqond it was computed on. Get a free key first (POST /api/demo-key/mint), then:

curl -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer zeq_ak_..." \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["KO42", "NM19"],
    "domain": "Newtonian Mechanics",
    "inputs": { "mass": 5, "acceleration": 9.81 }
  }'

Real response (abridged — value is the physics, the rest is the synchronized envelope):

{
  "value": 49.05,
  "unit": "N",
  "operator_id": "NM19",
  "zeqState": { "operators": ["KO42", "NM19"], "domain": "Newtonian Mechanics" },
  "master_sum": "Σ KO42 ⊕ NM19",
  "verification": { "precision_bound": "≤ 0.1%" },
  "zeqProof": "ea361108c408ff926c29ce8d9bca26c2e584725b…"
}

value is 5 × 9.81 = 49.05 N — verified live. Swap NM19 for NM21 ({"m1":5.972e24,"m2":7.348e22,"r":3.844e8} → 1.9821e20 N) or NM23 ({"mass":0.287,"velocity":5} → 3.5875 J) to compute gravity or kinetic energy through the same synchronized path.

Solver coverage

The Newtonian Mechanics domain has a live closed-form solver — the F=ma example above returns a real number today. Not every catalogued operator is wired to it: operators without solver support return no-match from /api/zeq/compute (unit no-match, no value). The catalogue rows are exact and documented regardless.

Extend it

Rigid body — chain NM28 + NM29 for gyroscopic stabilization with Zeqond-locked torque scheduling.
Orbital — pair NM19 + NM21 for multi-body orbital propagation with ≤0.1% drift across hours of integration.
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.

What it unifies​

Operator catalog​

Runnable worked example — F = ma, sealed to HulyaPulse​

Extend it​

Seeds​

Papers​