论文标题
最不舒服的旅程问题的概括
Generalization of the least uncomfortable journey problem
论文作者
论文摘要
直线上两个位置之间最不舒服的旅程的变化问题可以通过选择因变量来简化。结果表明，将位置而不是速度作为要确定的时间的最佳函数，可以消除等于术的约束。与因速度和因变量发现的结果相同的结果是以更简单，更简洁的方式获得的。接下来，该问题被概括为在任意曲线上运动。在加速引起的不适感的情况下，正如预期的那样，弯曲路径上的运动总是比直线上的运动更不舒服。目前尚不清楚这种混蛋引起的不适是这种情况，这似乎表明加速度比混蛋更合理地衡量了不适。研究了圆形路径上运动的示例。尽管我们无法通过分析解决问题，但是已经通过试验函数构建了近似解决方案，并且对于相关参数的某些选择，已经在数值上找到了精确的解决方案。
The variational problem of the least uncomfortable journey between two locations on a straight line is simplified by a choice of the dependent variable. It is shown that taking the position, instead of the velocity, as the optimal function of time to be determined does away with the isoperimetric constraint. The same results as those found with the velocity as the dependent variable are obtained in a simpler and more concise way. Next the problem is generalized for motion on an arbitrary curve. In the case of acceleration-induced discomfort, it is shown that, as expected, motion on a curved path is always more uncomfortable than motion on a straight line. It is not clear that this is necessarily the case for jerk-induced discomfort, which appears to indicate that the acceleration provides a more reasonable measure of the discomfort than the jerk. The example of motion on a circular path is studied. Although we have been unable to solve the problem analytically, approximate solutions have been constructed by means of trial functions and the exact solution has been found numerically for some choices of the relevant parameters.
