Critical Velocities of Ultracentrifuges Page: 4 of 14
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NACA TM 1272
From equations (2)
ak = A sin p (3)
OC = OC cos B
By linearizing, the-following equations are obtained:
P1 = A
l, =
(4)
ok Am@3
rl =C
Gz = CW
In equations (1), Lk = Lz = 0 but the moment of the external
forces applied to the rotor relative to the axis I is determined by
the expression
L - 611 h2 sin 13 + Gh sin P (5)
where 511 is the force applied at the end of the rotor spindle that
produces unit rotation in the case where the spindle is immovably
fixed, and G is the weight of the rotor; h and hi are shown in
figure 1.
By neglecting the gravitational force and by replacing sin 1
by 1
LI = - 511 h (6)
By substituting in the EulAr equation the values of the magnitudes
that are used, the following equation is obtained:
2 I - -11 h2J0 (7)mi
3
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Sokolov, V. I. Critical Velocities of Ultracentrifuges, report, March 1951; (https://digital.library.unt.edu/ark:/67531/metadc63029/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.