Download Advances in Fluid Mechanics by E. Krause PDF

By E. Krause

ISBN-10: 354011162X

ISBN-13: 9783540111627

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Shifting XYZ coils change their magnetic positioning equations. We define the shifted distances, xs and ys. We get new shifted coordinates (x′, y′, z) of the measurement point: x′ = x − xs y′ = y − ys Putting x′ and y′ into the positioning equations yields similar shifted positioning equations, because the coefficients of the coordinate variable P are not changed. 2 Rotating We substitute the E2 rotation matrix (see Chapter 2) in the Px, Py, and P expressions. The results are that the Px and Py expressions have the same transformation as x and y coordinates.

1:107ðHx½1Š + Hx½2ŠÞ − 0:2784ðHy½1Š − Hy½2ŠÞ − 0:1368Hx½3Š −ðxðHx½1Š − Hx½2ŠÞ + yðHy½1Š − Hy½2ŠÞ + zðHz½1Š − Hz½2ŠÞÞ = 0 CHAPTER 6 Quad Quadrilateral Coil Equations We use the same method for quad quadrilaterals as that for three quadrilaterals. 1 for four quadrilaterals a, b, c, and d. We add one equation for quadrilateral d from Eq. 2) G4d = G2c We can substitute Eq. 2 in Eq. 1 and then solve all G2. 2. Similar to Eq. 9, we get the positioning equation: MhaSSlbSSld + SSra Mhb SSlc SSld + SSra SSrb Mhc SSld + SSra SSrb SSrc Mhd = 0 Magnetic Positioning Equations.

6) Distortions and Disturbances 61 where ei½1Š2 = exi½1Š2 + eyi½1Š2 + ezi½1Š2 , ei½2Š2 = exi½2Š2 + eyi½2Š2 + ezi½2Š2 ; w[1] and w[2] are the weighting values, which may be wi½1Š = vi½1Šp and wi½2Š = vi½2Šp , and p can be any number, −2, −1, 0, 1, and 2. The constraints are Eqs. 3 and their Lagrange multipliers are p1/2, p2/2 and p3, and all the positioning equations and their Lagrange multipliers are q1…qn. 7) J is dependent on 9+7n variables Exx, Exy, Exz, Eyx, Eyy, Eyz, p1, p2, and p3 and n × qi and 3n × ei[1] and 3n × ei[2].

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