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By L H Erbe; Qingkai Kong; B G Zhang

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In fact this is the first step toward Lagrangian mechanics. The latter is a consequence of Newtonian mechanics that makes use of generalized coordinates to describe the motion of objects. It simplifies the solution of many problems. 1) as consequences of the dynamic equations for a system of particles. 2) are applied to continuous rigid bodies that occupy volumes or that are idealized as surface or linear mass distributions. 2) using a limit passage. However, these equations must be regarded as new axioms for rigid body mechanics.

From a logical standpoint, this particular combination of pictures is even “worse” than that of points and their position vectors. In applications, however, convenience always triumphs over formal requirements, so for mathematicians there is no recourse other than attempting to justify such “illegal” actions. Engineers often make use of objects or tools that are imperfect from a mathematical viewpoint. In the more extreme cases, entirely new branches of mathematics have been created in response to this.

1. 7) holds for all x ∈ X. Clearly, when a sequence {xn } converges to x0 in one norm then it also converges to x0 in any equivalent norm. 3. Show that any two norms in Rn are equivalent. December 24, 2008 44 10:59 World Scientific Book - 9in x 6in Introduction to Mathematical Elasticity Using some basis of a finite dimensional space, we can introduce a oneto-one correspondence between it and Rn or Cn that preserves algebraic operations and the norms. From this (and the equivalence of all norms on Rn or Cn ) it follows that on any finite-dimensional space all norms are equivalent.

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