On the problem of random vibrations, and of random flights in one, two, or three dimensions.
On the problem of random vibrations, and of random flights in one, two, or three dimensions.
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DOI：
10.1080/14786440408635894
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发表时间：
1919-04-01
影响因子：
1.6
通讯作者：
Rayleigh
中科院分区：
文献类型：
--
作者：
Rayleigh
当一个单位振幅的等周期振动被组合时，结果取决于分配给各个相位的值。当相位是随机的时，合成振幅是不确定的，并且所有可以说的都与各种振幅（r）的概率有关，或者更严格地说，振幅位于极限r和r~ dr内的概率。n非常大的重要情况~很久以前就考虑过~”，结论是所讨论的概率简单地为2-e-~/~ rdr........ (i)结果的相位（δ）当然是不确定的，所有的值都是等概率的。该方法随后开始的假设，单位分量的相位被限制为0和180，随机采取，使点（r，0），代表振动，躺在轴0= 0，和无差别的两侧的原点。结果x，beil）g是差
W HEN a nmnber (n) o [isoperiodic vibrations of unit amplitude are combined, the resultant depends upon the values assigned to the individual phases. When the phases are at random, the resultant amplitude is indeterminate, and all that can be said relates to the probability o {'various amplitudes (r), or more strictly to the probability that the amplitude lies within the limits r and r~ dr. The important case where n is very great~ considered a long time ago~" with the conclusion that the probability in question is simply2-e-~/~ rdr........(i) nThe phase (8) of tile resultant is of course indeterminate, and all values are equally probable. The method then followed began with the supposition that the phases of the unit components were limited to 0 and 180 taken at, random, so that the points (r, 0), representative of the vibrations, lie on the axis 0= 0, and indifferently on both sides of the origin. The resultant x, beil) g the difference