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Mechanics operators

16 operators in the mechanics 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
LD92Constrained Lagrangian with Lagrange multiplier for holonomic constraint enforcement.L_D = \frac{1}{2}m\dot{q}^2 - V(q) - \lambda g(q)
LNM21Newtonian-Lagrangian mechanics: Lagrangian as kinetic minus potential energy for particle dynamics.\mathcal{L}_{NM} = T - V = \frac{1}{2}m|\dot{\vec{r}}|^2 - V(\vec{r})
TCP2Simple pendulum period: 2pi times square root of length over gravitational acceleration.T_2 = 2\pi\sqrt{\frac{L}{g}}
TRB1Coulomb friction law: friction force equals friction coefficient times normal force.F_f = \mu N
TRB10Pressure-dependent friction coefficient model for boundary lubrication.\mu = \mu_0 + k P
TRB2Real contact area: ratio of applied load to material hardness for rough surface contact.A_r = \frac{W}{H}
TRB3Hertz contact pressure: maximum pressure in elastic contact between curved surfaces.P_{max} = \frac{3W}{2\pi a^2}
TRB4Hertz contact radius for elastic contact between a sphere and a plane.a = \left(\frac{3WR}{4E^*}\right)^{1/3}
TRB5Hydrodynamic lubrication film thickness from Reynolds equation for bearing design.h = \frac{3\mu U L}{W}
TRB6Lambda ratio: minimum film thickness relative to composite surface roughness for lubrication regime.\Lambda = \frac{h_{min}}{\sqrt{\sigma_1^2 + \sigma_2^2}}
TRB7Archard wear equation: volumetric wear proportional to load, sliding distance, and inversely to hardness.W = K \frac{F_N \cdot s}{H}
TRB8Specific wear rate: volume of material removed per unit normal force per unit sliding distance.k = \frac{V}{F_N \cdot s}
TRB9Shear strength of a tribological interface: base shear stress plus pressure-dependent term.\tau = \tau_0 + \alpha P
TX0Thermal decay operator: exponential temperature decrease with characteristic time constant.φ × 8πγlₚ²√(j(j+1))
UF2Elastic potential energy stored in a spring: one-half k times displacement squared.U_2 = \frac{1}{2}kx^2
YRA01Harmonic velocity amplitude: peak velocity of an oscillating system.Y_R = A\omega\cos(\omega t)

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":["LD92"],"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​