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In mathematics, physics, and theoretical computer graphics, tapering is a kind of shape deformation. [1] [2] Just as an affine transformation, such as scaling or shearing, is a first-order model of shape deformation, tapering is a higher order deformation just as twisting and bending. Tapering can be thought of as non-constant scaling by a ...
The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).
Mean aerodynamic chord (MAC) is defined as: [6] = (), where y is the coordinate along the wing span and c is the chord at the coordinate y.Other terms are as for SMC. The MAC is a two-dimensional representation of the whole wing. The pressure distribution over the entire wing can be reduced to a single lift force
The so-called "Planck-taper" window is a bump function that has been widely used [53] in the theory of partitions of unity in manifolds. It is smooth (a C ∞ {\displaystyle C^{\infty }} function) everywhere, but is exactly zero outside of a compact region, exactly one over an interval within that region, and varies smoothly and monotonically ...
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
The beam is originally straight and slender, and any taper is slight; The material is isotropic (or orthotropic), linear elastic, and homogeneous across any cross section (but not necessarily along its length) Only small deflections are considered; In this case, the equation describing beam deflection can be approximated as:
In laser physics, numerical aperture is defined slightly differently. Laser beams spread out as they propagate, but slowly. Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field".