最高柱--相似解的动力系统方法
The Tallest Column -- A Dynamical System Approach using a Similarity Solution
摘要：
一个经典的问题，最高的柱的设计，再次使用不同的方法解决。利用相似解对方程进行了变换，去掉了端点处的奇异性。由此产生的自治系统有一个临界点和解决方案必须在其稳定的流形。通过在稳定流形的方向上的临界点附近开始并向后数值求解来找到解决方案。这消除了以前使用的迭代积分方法的需要。所示的方法工作的夹紧或铰接的边界条件，也可以用于其他问题，涉及奇点的端点。
英文摘要：
A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the direction of the stable manifold, and solving backwards numerically. This removes the need for an iterative integration method that was previously used. The method is shown to work for clamped or hinged boundary condition and can also be used for other problems involving singularities at the endpoints.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
