AIAA 2002-5664 Analysis Design and Optimization of

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Extra resources for AIAA 2002-5664 Analysis Design and Optimization of Non-Cylindrical Fuselage for Blended-Wi

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Then we get the configuration ( c 1 , . . , c n - 1 ). Then shift cyclically thefirstm coins u times. , c n - 1 ). Then u is covered by cm. Therefore, removing cm+1 of m +1, we may put a copy of cm tom + 1. , c n - 1 ). Now we shift right cyclically the first m coins m — u times reaching (c1, c 2 , . . , c n - 1 ). The next treatment is that, in consecutive steps, remove the coin ci of i and then 34 Chapter 2. , 2. Finally, remove the coin c\ of 1 and put a copy of the coin cn-1 of n to 1. Then we reach the configuration ( c n - 1 , c 1 , .

C n - 1 ). Shift the coins right cyclically n — 1 times reaching (c 2 , c 2 , c 3 , . . , c n - 1 , c 1 ). Now we can shift the first m coins right cyclically m — 1 times, which results in ( c 2 , . . , c n - 1 , c 1 ). We exchange the coin c2 of the first vertex for a copy of c1 covering the last vertex. Finally, shift again the first m coins right cyclically, obtaining the configuration (c2, c1, c 3 , . . , cn-1 ,c 1 ). 1. , m — 1, m + 1 , . . , n) [shifting first m right cyclically], F ( l , .

In other words, we can also consider the application of D(l)-compatible permutations. We should also take observations to rule (2). Suppose that a vertex vk is covered by a coin cj and we apply rule (2) consecutively twice such that we change a coin cj of the vertex vk for cland then immediately after change the coin a of vk for ci. Of course, we have the same result of these two consecutive steps if we omit the first one and change the coin cj of vk for ci directly. Assume now that, applying rule (2), we change the coin cj of the vertex vk for cl, and after this, applying one or more consecutive rules of type (1), we move coin cl to a vertex vu, and finally we change the coin cl of vu for ci, applying again rule (2).

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