#statics

Centre-of-mass and barycentre mechanics as an API, computed locally and deterministically. The point-masses endpoint computes the centre of mass of a system of point masses in one, two or three dimensions, applying x_com = Σ(m_i·x_i)/Σm_i to each axis from a list of masses and their x (and optional y and z) coordinates — masses of 1, 2 and 3 at positions 0, 1 and 2 give a centre of mass at 1.333, and four equal masses at the corners of a square sit at its centre. The two-body endpoint computes the barycentre of two masses separated by a distance, r1 = d·m2/(m1+m2) from the first body, which always lies closer to the heavier one — for the Earth-Moon system the barycentre is about 4 670 km from Earth’s centre, still inside the planet. Lists may be passed as comma-separated values (masses=1,2,3&x=0,1,2) or as JSON arrays in a POST body, and units are consistent and unit-agnostic. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics, engineering-statics, astronomy, robotics, game-physics and mechanics-education app developers, balance-point and barycentre tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 2 endpoints. This is the centre of mass; for the rotational moment of inertia use a moment-of-inertia API.

api.oanor.com/centerofmass-api

Estática y dinámica de plano inclinado y fricción como una API, calculada local y determinísticamente. El endpoint de inclinación analiza un bloque en una rampa: a partir de una masa, el ángulo de inclinación y un coeficiente de fricción, devuelve la fuerza normal N = m·g·cosθ, la componente de la gravedad a lo largo de la pendiente m·g·sinθ, la fricción estática máxima μ·N, si el bloque permanece quieto o se desliza (se desliza cuando tanθ > μ) y, si se desliza, la fuerza neta y la aceleración a = g·(sinθ − μ·cosθ). El endpoint de fricción maneja una superficie plana: la fuerza de fricción f = μ·N (la fuerza normal dada directamente o a partir de una masa), el ángulo de reposo atan(μ), y — dada una fuerza aplicada — si el objeto se mueve y su aceleración. El endpoint de rampa proporciona la fuerza necesaria para mover una carga hacia arriba o hacia abajo por una rampa a velocidad constante, F = m·g·(sinθ ± μ·cosθ), la fuerza sin fricción, la eficiencia y si la rampa es autoblocante. La gravedad por defecto es 9.80665 m/s² y se puede anular. Todo se calcula local y determinísticamente, por lo que es instantáneo y privado. Ideal para herramientas de educación en física y mecánica, manejo de materiales, diseño de transportadores y rampas, y aplicaciones de estática en ingeniería. Cálculo local puro — sin clave, sin servicio de terceros, instantáneo. En vivo, nada almacenado. 3 endpoints. Esto es fuerzas de plano inclinado con fricción; para la ventaja mecánica ideal (sin fricción) de máquinas simples, use una API de palanca.

api.oanor.com/incline-api

杠杆、力矩平衡和简单机械的机械优势计算作为API，本地确定性地计算。杠杆端点应用杠杆定律，力·力臂 = 负载·负载臂，并求解你省略的力、负载、力臂或负载臂中的任意一个，返回机械优势MA = 力臂/负载臂 = 负载/力，以及杠杆是增力还是增速。力矩端点计算单个力矩，M = F·d，或平衡一个绕支点的跷跷板：根据每侧的力和距离，告诉你是否平衡、净力矩和旋转方向，或者求解你省略的一个值以达到平衡。机械端点给出简单机械的理想机械优势——斜面（长度/高度）、螺丝（2πR/螺距）、轮轴（R/r）、楔子（长度/厚度）或滑轮系统（支撑绳数）——并在给定效率和力的情况下，给出实际机械优势和输出力。所有计算都在本地确定性地进行，因此即时且私密。非常适合物理和工程教育工具、力学和静力学应用、机械设计和DIY计算器。纯本地计算——无需密钥，无需第三方服务，即时。实时，不存储任何内容。3个端点。这是杠杆和简单机械的机械优势；对于齿轮和皮带传动比，请使用齿轮或皮带传动API。

api.oanor.com/lever-api

Beam statics as an API, computed locally and deterministically. The simply-supported endpoint analyses a beam on two supports under a point load (anywhere along the span) or a uniformly distributed load: it returns the support reactions, the maximum shear and the maximum bending moment with its location, and — if you pass the Young's modulus E and second moment of area I — the maximum deflection. The cantilever endpoint does the same for a beam fixed at one end, returning the reaction force and fixing moment, the maximum bending moment and the free-end deflection. The section endpoint gives the cross-section properties that those deflections need: the second moment of area (moment of inertia) and the section modulus for a rectangle, a solid circle or a hollow circular pipe. Every result lists the formula used, so you can show your working. Use consistent units — in SI, load in newtons, distributed load in N/m, lengths in metres, E in pascals and I in m⁴ give moments in N·m and deflections in metres. Everything is computed locally and deterministically, so it is instant and private. Linear-elastic, small-deflection theory — a learning and estimating tool, not a substitute for a qualified structural engineer on a real design. Ideal for engineering and architecture tools, education and physics apps, maker and DIY calculators, and CAD helpers. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is structural beam statics; for bolt and fastener torque use a torque API.

api.oanor.com/beam-api