Read e-book online Dynamics of Flexible Spacecraft: Department of General PDF

By Peter W. Likins, Robert E. Roberson, Jens Wittenburg (auth.)

ISBN-10: 3211811990

ISBN-13: 9783211811993

ISBN-10: 3709129087

ISBN-13: 9783709129081

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Read Online or Download Dynamics of Flexible Spacecraft: Department of General Mechanics Course held in Dubrovnik, September 1971 PDF

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Extra info for Dynamics of Flexible Spacecraft: Department of General Mechanics Course held in Dubrovnik, September 1971

Example text

Dtry 5 5 5 where M5 is the total mass of the s th finite element, one can de fine the (3x6N) matrix W! as the matrix W5 evaluated for the element mass center coordinates ~: , '1 ~ , t; ~ and write (41) Eq. (34) can now be rewritten in terms of the notation of Eqs. d'lr s 33 +JwTCC[c+2w(a (~ +ww)c]J-1-d'lr s +M5 w:r {CC0X +C 5 C(~ + ww)R] +C\~a + wawa)R:} - jw\G- Drilr)du +jwr Dr if'dv . (42) s Eq. (42) is still not in the desired final form for -s L , because the dependence of c on y 5 has not yet been ex- plicitly accomodated (see Fig.

N i\{ i\n t h e rna tr1ces 't , ... , -E y are compr1se u. , 1 -~ . . - . ~ and jl ~ by U. " and /l = C~ , ~ = i ,... , n • Thus Eq. (53), with substitutions from Eq. (46), provides 3n sea! 3. Substructure Equations of Motion 38 ar second order differential equations in the 6 N unknowns u,~, ... , ) n { u,~'~"', ... ,fi~ (« = 1, 2,3 • Completion of the set requires the equations of rotational motion of the nodal bodies. The basic equation for the rotation of the Jth no dal rigid body is . J"" the angular momentum, and 0~ the inertia dyadic of the nodal body, all referred to the mass center of the body, and over-dot denotes time differentiation in an inertial frame of reference.

I develops. l. With the 53 Spin Effects on Modes definitions wi ~k11in, A~~ k2/m, W~ ~ k3/m, Eqs. 2 + w~ u. 1. 3 (86) =0 (87) =0 . (88) In case b), on the other hand, the preload in the spring identified by k2 has no influence on the restoring forces developed after displacement u. 1 - .. 3+W3Ll3 = =0 · (91) In case c) the preloau in the increase displacements u.. 2 = 0 ( 93) U. U. 2 + (wf - 2 n 2 )u. 3 =0 . (94) Thus we can see that the influence of spin-induced preloads is dependent upon the structural configuration, acting sometimes to stiffen the structure (and elevate its natural frequency), and sometimes to soften it (reducing the natural frequen- 54 6.

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Dynamics of Flexible Spacecraft: Department of General Mechanics Course held in Dubrovnik, September 1971 by Peter W. Likins, Robert E. Roberson, Jens Wittenburg (auth.)


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