By Y. Gan

ISBN-10: 9535104470

ISBN-13: 9789535104476

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Extra resources for Continuum Mechanics - Progress in Funds., Engrg. Applns.

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N in the linear Spencer sequence. 2. The passage from χq to τq is exactly the one done by E. and F. Cosserat in ([C], p 190). 3. 4. For any section f q+1 ∈ Rq+1 , the transformation: ¯ f q +1 χq −→ χq = f q−+11 ◦ χq ◦ j1 ( f q ) + D ¯ χq = 0. is called a gauge transformation and exchanges the solutions of the ﬁeld equations D Introducing the formal Lie derivative on Jq ( T ) by the formulas: L(ξ q+1 )ηq = {ξ q+1 , ηq+1 } + i (ξ ) Dηq+1 = [ξ q , ηq ] + i (η ) Dξ q+1 ( L( j1 (ξ q+1 ))χq )(ζ ) = L(ξ q+1 )(χq (ζ )) − χq ([ξ, ζ ]) and passing to the limit with f q+1 = idq+1 + tξ q+1 + ...

Refer to a Cartesian coordinate system (o-xy). Besides the Euler coordinate x and y, the arc length s, being a Lagrange coordinate, is also employed as a variable in our analysis. The slope angle of the elastica at an arbitrary point is  , which continuously changes from 0 at its left end to 90 at the right end. The bending stiffness of the elastica is EI, where I is the inertial moment of the cross section, and E  E 1   2 , with E being the Young’s modulus and  the Poisson’s ratio of the material.

Math. , 75, 1965, 1-114. [34] I. Stewart: Galois Theory, Chapman and Hall, 1973. P. Teodorescu: Dynamics of Linear Elastic Bodies, Editura Academiei, Bucuresti, Romania; Abacus Press, Tunbridge, Wells, 1975. [36] E. Vessiot: Sur la théorie des groupes inﬁnis, Ann. Ec. Norm. , 20, 1903, 411-451. [37] E. Vessiot: Sur la théorie de Galois et ses diverses généralisations, Ann. Ec. Norm. , 21, 1904, 9-85. [38] C. Yang: Magnetic monopoles, ﬁber bundles and gauge ﬁelds, Ann. New York Acad. Sciences, 294, 1977, 86.