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Newtonian operators

14 operators in the newtonian category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
NM18Newton's first law: with zero net force a body's velocity stays constant.∑F⃗ = 0 ⇒ v⃗ = const
NM19Newton's second law relating net force to mass times acceleration, F = ma.F⃗ = m⃗a
NM20Newton's third law: the forces two bodies exert on each other are equal and opposite.F₁₂ = -F₂₁
NM21Newton's law of universal gravitation between two point masses.F = Gm₁m₂/r²
NM22Mechanical work done by a force acting over a displacement, W = F·d.W = ∫F⃗·d⃗s
NM225Generalized force summation over 225 bodies, extending Newton's laws to large many-body systems.F_{225} = \sum_{i=1}^{225} m_i a_i
NM23Translational kinetic energy of a moving mass, KE = ½mv².K = ½mv²
NM24Gravitational potential energy near a planetary surface, PE = mgh.U_g = mgh
NM25Conservation of mechanical energy: the sum of kinetic and potential energy is constant.K_i + U_i = K_f + U_f
NM26Linear momentum defined as mass times velocity, p = mv.p⃗ = m⃗v
NM27Conservation of total linear momentum in an isolated system.Δp⃗_total = 0
NM28Angular momentum as the cross product of position and linear momentum, L = r × p.L⃗ = r⃗ × p⃗
NM29Torque as the cross product of position and applied force, τ = r × F.τ⃗ = r⃗ × F⃗
NM30Hooke's-law restoring force and the resulting simple-harmonic motion.F⃗ = -k⃗x

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["NM18"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​