By Jack Goldstein
In this extraordinary book you'll find a couple of hundred proof concerning the human physique. Separated into sections comparable to the mind, imaginative and prescient, bones and plenty of extra you can find a few interesting details inside!
Whether you're engaged on a human biology undertaking otherwise you simply need to know extra approximately how your physique works, this can be a good addition in your bookshelf.
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Extra info for 101 Amazing Facts About The Human Body
Setting Fi ðα1 ; α2 Þ ¼ 0 from Eq. 9) for the displacement vector, we have ∗ m m = mz ∗ S ρ2′ r2 Mz ∗ M Sz ∗ α2 ρ1′ α∗ 2 α∗ 1 r1 Hz m r2 α2 M(αi) r1 α1 S Fig. 2 Fictitious deformation of the surface. 34 Shells of complex geometry νðα1 ; α2 Þ ¼ Hðα1 ; α2 Þm: (2:29) Ã from the surface S to S . Evidently, the measured along m Here Hðαi Þ is the distance Ã vector equation of S can be written as Ã r ¼ rðα1 ; α2 Þ þ Hðα1 ; α2 Þm: Let (2:30) Ã Hðα1 ; α2 Þ ¼ Hz þ Hðα1 ; α2 Þ: (2:31) Then, on substituting Eq.
By substituting Eqs. 28) are used to calculate the Christoffel symbols Ãk Ã ðzÞk Gij on S . Gij are calculated from Eqs. 27) by replacing Azi and their derivatives for Ai and @Ai =@α1;2 , respectively. Ã in Fig. 3. Let a For example, consider a shell of complex geometry S as shown Ã cylinder ofÃ constant radius R0 be the reference surface for S. 30). Introduce polar coordinates α1 and α2 on S, such that α1 is the axial and α2 is the polar angular coordinate. They are related to the global Cartesian coordinates by 40 Shells of complex geometry À Á rðαi Þ ¼ xi þ yj þ z k ¼ R0 i sin α2 þ k cos α2 þ α1 j: (2:59) The Lamé parameters Ai and curvatures kij are given by A1 ¼ 1; k11 ¼ 1=R1 ¼ 0; A2 ¼ R0 ; k12 ¼ 0; k22 ¼ 1=R2 ¼ 1=R0 : (2:60) For the coefﬁcients θi ¼ 1 þ Hðαi Þ=Ri we have θ1 ¼ 1; θ2 ¼ 1 þ Hðαi Þ=R0 : (2:61) Hence, from Eq.
3 The extrinsic geometry of the surface and a local base fn; nb ; τ g associated with a curve Γ. τ ¼ dr dα1 dα2 þ r2 : ¼ r1 ds ds ds (1:13) By applying the Frenet–Serret formula for the derivative of τ with respect to s we get n dτ ¼ ; ds Rc (1:14) n is the vector normal to Γ. By substituting Eq. 8) we obtain n¼ 2 X 2 X i¼1 k¼1 rik dαi dαk dα2 dα2 þ r1 1 þ r2 2 ; ds ds ds ds (1:15) where rik ¼ @2r @2r ¼ ; @αi @αk @αk @αi rik ¼ rki : and n such that m n ¼ cos j. Then the Let φ be the angle between the vectors m yields scalar product of Eq.
101 Amazing Facts About The Human Body by Jack Goldstein