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A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol ″, [2] is a unit of angular measurement equal to 1 / 60 of a minute of arc, 1 / 3600 of a degree, [1] 1 / 1 296 000 of a turn, and π / 648 000 (about 1 / 206 264.8 ) of a radian.
[2] In experimental fluid dynamics, the Stokes number is a measure of flow tracer fidelity in particle image velocimetry (PIV) experiments where very small particles are entrained in turbulent flows and optically observed to determine the speed and direction of fluid movement (also known as the velocity field of the fluid). For acceptable ...
The correct branch of the multiple valued function arctan x to use is the one that makes ν a continuous function of E(M) starting from ν E=0 = 0. Thus for 0 ≤ E < π use arctan x = arctan x, and for π < E ≤ 2π use arctan x = arctan x + π. At the specific value E = π for which the argument of tan is infinite, use ν = E.
A milliradian (SI-symbol mrad, sometimes also abbreviated mil) is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). ). Milliradians are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel (up, down, left, or
Here Z F is the acoustic impedance of the film (Z F = ρ F c F = (ρ F G f) 1/2)= (ρ F /J f) 1/2), k F is the wave vector and d F is the film thickness. J f is the film's viscoelastic compliance, ρ F is the density. The poles of the tangent (k F d F = π/2) define the film resonances. [55] [56] At the film resonance, one has d F = λ/4. The ...
Solving (1) is an elementary differential equation, thus the steps leading to a unique solution for v x and, subsequently, x will not be enumerated. Given the initial conditions v x = v x 0 {\displaystyle v_{x}=v_{x0}} (where v x0 is understood to be the x component of the initial velocity) and x = 0 {\displaystyle x=0} for t = 0 {\displaystyle ...
Setting a 2 = 2m − 3 makes the variance equal to unity. Then the only free parameter is m , which controls the fourth moment (and cumulant) and hence the kurtosis. One can reparameterize with m = 5 / 2 + 3 / γ 2 {\textstyle m=5/2+3/\gamma _{2}} , where γ 2 {\displaystyle \gamma _{2}} is the excess kurtosis as defined above.
Substituting the small angle approximations, and exploiting that the product of a small angle squared, in radians, with the friction coefficient, θ 2 μ, is insignificant (for a steep 20% slope and a good friction coef. of 0.8, this equals (.2) 2 x0.8≈0.03):