By Lyakhova S.L.

The systematic research of the equations of movement for debris of a rotating medium used to be initiated through Sobolev [1, 2]. those equations vary from the normal Navier-Stokes equations in that they include the time period [v, w], the vector made of the rate via the angular rotation speed, which takes account of the rotation of the reference procedure.

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Additional info for A cauchy problem with discontinuous initial data modeling propagation of vibrations in a rotating viscous compressible fluid

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1. AMPLIFIERS ARMATURE v2 vo kr(1 + τ2 s) + s(1 + τ3 s) k1k5 v1 1 + τ1 s + _ _ kc kf ki(1 + τ4 ) s(1 + τ5 s) + _ vs MOTOR AND REDUCER TN io _ 1 Ra + La s km + kb ωm kt 1/N 1 ωm Jm s + _ ωm N Fig. 7304 kg Ns [s] [s] [s] [s] [s] [s] T ω 26 2 Analytical Models Velocity Command 1 Torque Velocity Command Pinion velocity y(n) = Cx(n)+Du(n) x(n+1) = Ax(n)+Bu(n) 1 Encoder Antenna Structure Drive pinion velocity Fig. 9 Velocity loop model magntiude 100 10–1 10–2 10–3 from analysis from identification 10–1 100 frequency, Hz 101 Fig.

Thus, the antenna structure needs to be represented in this form, to allow the use of control system software such as Matlab or Simulink. The modal state-space 18 2 Analytical Models (a) (b) (c) (d) Fig. 87 Hz). For each mode the nodal displacements are sinusoidal, have the same frequency, and the displacements are shown at their extreme values. Gray color denotes undeformed state representation of the antenna structure is a triple ( Am , Bm , Cm ) characterized by the block-diagonal state matrix, Am ; see [2] ⎡ × × 0 0 ··· ··· 0 0 ⎢ × × 0 0 ··· ··· 0 0 ⎢----------------------------⎢ ⎢ 0 0 × × ··· ··· 0 0 ⎢ ⎢ 0 0 × × ··· ··· 0 0 ⎢ Am = diag(Ami ) = ⎢ - - - - - - - - - - - - - - - - - - - - - - - - - - - - ⎢··· ··· ··· ··· ··· ··· ··· ··· ⎢ ⎢··· ··· ··· ··· ··· ··· ··· ··· ⎢ ⎢----------------------------⎣ 0 0 0 0 ··· ··· × × 0 0 ··· ··· × × 0 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥, ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ i = 1, 2, .

The magnitude of the velocity loop transfer function is shown in Fig. 10, solid line. 5 Drive Parameter Study In this section the effect of the drive inertia and stiffness on the antenna velocity loop properties is investigated. The inertia of the drive includes motor, brake, and gearbox, and the drive stiffness includes gearbox stiffness and shaft stiffness. Because the motor dominates the drive inertia, the motor inertia is investigated, and because gearbox stiffness dominates the drive stiffness, the drive stiffness is investigated.

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A cauchy problem with discontinuous initial data modeling propagation of vibrations in a rotating viscous compressible fluid by Lyakhova S.L.


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