# Download e-book for kindle: Theory of orbits. The restricted problem of three bodies by Victory Szebehely

By Victory Szebehely

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1. The geometry of the vibrating strip. We suppose that the strip is rigidly supported at the ends xl = ±d . 19) into account, we fmd after a series of transformations the following expressions for a nm and b nm : b e)( 21tnm . 20) in the form. 00 rn I;cmLOmP m=l (2 -Om2)+8 2b nm ]=0, 0) n,m=1,2, ... ,oo. 21) 32 CHAPTER 1 We now analyze two particular cases with respect to the values of parameters 2dA- 1 and fA-1 . e. d = MA/2. For this case sin(1t2dlA) = 0 and hence b nm = 0 except when m ± n = M .

Cr(2) - 0 . cr(2) - 0 cr 12 - , 11 - , 22 - . 24) give us the following expressions, including the zeroth, fIrst, and second approximations: ul = E 't )A 0 -2G 0 -cosS, 0 0 (0 All -A12 12 A II G 12 7t 't [ (A 'tC. 'tC u2 =-0- xl +E 2 --0-sm2S---0-XI 47t G 12 2G 12 G 12 II . 25) also occur. 3. PURE SHEAR IN THE OXlx3 PLANE (Fig. 5. 5. Here, for completeness we give the fmal results including the zeroth, fIrst and second approximations. 8. Quasi-homogeneous States Corresponding to Tension-Compression We will examine the quasi-homogeneous stress states corresponding to tension-compression along different coordinate axes.

00, ex = 1,2,3. 6) a set of homogeneous algebraic equations for the constants f crn [o~p(0)2 rn=1 n~)+ Ea nrn + E2b nrn ]= 0, n = 1,2, ... jn )dV . 16) nrn is the natural frequency of the m-th mode of the body with rectilinear orthotropy. 1 (0). 13), are symmetric. 2. AN EXAMPLE As an example, we consider the strip Ix 11 ::; d which is infmite in the directions of the oX 2 and oX 3 axes (Fig. 1). Note that the oX 3 axis is directed perpendicularly 31 PLANE-CURVED COMPOSITES to the plane of Fig.