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https://www.engineeringnotes.org/metrology/airy-points-and-bessel-points/
Airy points and Bessel points are commonly used in precision engineering to support bodies. These two points define the location where a support has to be placed to minimise distortion. Airy points and Bessel points are commonly used in precision engineering to support bodies.
http://www.mechanicsandmachines.com/?p=330
Bessel points are the support points which minimize the change in length of the beam. A beam will undergo a length change as it bends given by The Bessel points are located at 0.2203 L from each end.
http://www.mechanicsandmachines.com/?tag=bessel-points
The answer depends on the desired objective. Below we describe some of the most common support locations: Airy points, Bessel points, minimum deflection, and nodal points. It turns out that these points are relatively close to each other for the uniform beam. The …
https://en.wikipedia.org/wiki/Airy_points
To support a line standard, one wishes to minimise the linear, rather than angular, motion of the ends. The Bessel points (after Friedrich Bessel) are the points at which the length of the beam is maximized. Because this is a maximum, the effect of a small positioning error is proportional to the square of the error, an even smaller amount.
https://support.office.com/en-us/article/BESSELK-function-606D11BC-06D3-4D53-9ECB-2803E2B90B70
The n-th order modified Bessel function of the variable x is: where Jn and Yn are the J and Y Bessel functions, respectively. Example. Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter.
https://www.mathworks.com/help/symbolic/mupad_ref/besselj.html
besselJ(v, z) represents the Bessel functions of the first kind: The Bessel functions are defined for complex arguments v and z. A floating-point value is returned if either of the arguments is a floating-point number and the other argument is numerical. For most exact arguments the Bessel functions return an unevaluated function call.
https://support.office.com/en-us/article/BESSELJ-function-839CB181-48DE-408B-9D80-BD02982D94F7
This article describes the formula syntax and usage of the BESSELJ function in Microsoft Excel. Description. Returns the Bessel function. Syntax. BESSELJ(X, N) The BESSELJ function syntax has the following arguments: X Required. The value at which to evaluate the function. N Required. The order of the Bessel function.
http://m.blog.naver.com/ezcmm/110151863636
Bessel points are used for two-point support, and minimize the change in the overall length.
https://en.wikipedia.org/wiki/Bessel_beam
The properties of Bessel beams make them extremely useful for optical tweezing, as a narrow Bessel beam will maintain its required property of tight focus over a relatively long section of beam and even when partially occluded by the dielectric particles being tweezed.
https://supportcenter.checkpoint.com/
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