By Victory Szebehely
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Extra info for Theory of orbits. The restricted problem of three bodies
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.
Theory of orbits. The restricted problem of three bodies by Victory Szebehely