Newtonian operators

14 operators in the newtonian category of the live registry. Compose them in a contract or call POST /api/zeq/compute — KO42 is always on, plus up to three more per call.

How it computes: dedicated closed-form solver solveCM — real equations over CODATA-2018 constants; where an operator needs a series/matrix/field a scalar cannot express, it refuses honestly. See the solvers.

Operator	Description	Equation
`NM18`	Newton's first law: with zero net force a body's velocity stays constant.	`∑F⃗ = 0 ⇒ v⃗ = const`
`NM19`	Newton's second law relating net force to mass times acceleration, F = ma.	`F⃗ = m⃗a`
`NM20`	Newton's third law: the forces two bodies exert on each other are equal and opposite.	`F₁₂ = -F₂₁`
`NM21`	Newton's law of universal gravitation between two point masses.	`F = Gm₁m₂/r²`
`NM22`	Mechanical work done by a force acting over a displacement, W = F·d.	`W = ∫F⃗·d⃗s`
`NM225`	Generalized force summation over 225 bodies, extending Newton's laws to large many-body systems.	`F_{225} = \sum_{i=1}^{225} m_i a_i`
`NM23`	Translational kinetic energy of a moving mass, KE = ½mv².	`K = ½mv²`
`NM24`	Gravitational potential energy near a planetary surface, PE = mgh.	`U_g = mgh`
`NM25`	Conservation of mechanical energy: the sum of kinetic and potential energy is constant.	`K_i + U_i = K_f + U_f`
`NM26`	Linear momentum defined as mass times velocity, p = mv.	`p⃗ = m⃗v`
`NM27`	Conservation of total linear momentum in an isolated system.	`Δp⃗_total = 0`
`NM28`	Angular momentum as the cross product of position and linear momentum, L = r × p.	`L⃗ = r⃗ × p⃗`
`NM29`	Torque as the cross product of position and applied force, τ = r × F.	`τ⃗ = r⃗ × F⃗`
`NM30`	Hooke's-law restoring force and the resulting simple-harmonic motion.	`F⃗ = -k⃗x`

Compute one — a real call

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["NM19"],"inputs":{"m":10,"a":3}}'

Returns 30 N — with unit, uncertainty, the generated master equation, and a signed envelope you can verify.

Compute one — a real call​

See also​

Compute one — a real call

See also