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http://www.mechanicsandmachines.com/?p=330
The Bessel points are located at 0.2203 L from each end. A good discussion of Airy points, Bessel points, and minimum gravity sag is given in the thesis by Nijsse at TU Delft, Linear motion systems: a modular approach for improved straightness performance.
http://www.mechanicsandmachines.com/?tag=bessel-points
One common question is “what are the optimal support locations for a beam?” 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.
https://www.engineeringnotes.org/metrology/airy-points-and-bessel-points/
Bessel Points. In case we are trying to minimise the maximum extent the member deflects from the centre line, then the bessel point should be used for support instead. Bessel Points can be calculated using the following formula. \( s =0.559L \) Application: Support of Length Standards
https://www.practicalmachinist.com/vb/machine-reconditioning-scraping-and-inspection/airy-points-bessell-points-339219/
Aug 26, 2017 · To properly support a surface plate you use Bessell points. The Bessel points will support an evenly-loaded bar or plate at the point of minimum deflection. Airy points are 1/ square root of 3 = 0.577L Bessell points are given as 0.554L The text doesn't say how that number was derived.
http://www.cs.sjsu.edu/~beeson/courses/Ma133a/ch5.8.pdf
Ch 5.8: Bessel’s Equation!! Bessel Equation of order ν: ! Note that x = 0 is a regular singular point. ! Friedrich Wilhelm Bessel (1784 – 1846) studied disturbances in planetary motion, which led him in 1824 to make the first systematic analysis of solutions of this equation. The …
https://www.mathworks.com/help/matlab/ref/besselj.html
J = besselj(nu,Z,scale) specifies whether to exponentially scale the Bessel function of the first kind to avoid overflow or loss of accuracy.If scale is 1, then the output of …
https://db0nus869y26v.cloudfront.net/en/Airy_points
Those would be the Bessel points of a beam 1020 mm long. Other support points of interest. Other sets of support points, even closer than the Bessel points, which may be wanted in some applications are: The points for minimum sag, 0.5536 times the length.
https://en.wikipedia.org/wiki/Bessel_function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation + + (−) = for an arbitrary complex number α, the order of the Bessel function. Although α and −α produce the same differential equation, it is conventional to define different Bessel functions for these two values ...
https://la.mathworks.com/help/matlab/ref/besselj.html
J = besselj(nu,Z,scale) specifies whether to exponentially scale the Bessel function of the first kind to avoid overflow or loss of accuracy.If scale is 1, then the output of …
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