In the book `What is Mathematics?' Richard Courant and Herbert Robbinspresented a solution of a Whitney's problem of an inverted pendulum on arailway carriage moving on a straight line. Since the appearance of the book in1941 the solution was contested by several distinguished mathematicians. Thefirst formal proof based on the idea of Courant and Robbins was published byIvan Polekhin in 2014. Polekhin also proved a theorem on the existence of aperiodic solution of the problem provided the movement of the carriage on theline is periodic. In the present paper we slightly improve the Polekhin'stheorem by lowering the regularity class of the motion and we prove a theoremon the existence of a periodic solution if the carriage moves periodically onthe plane.
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机译：在书中“是什么数学？” Richard Courant和Herbert Robbinspresented在一条直线上移动的Arailway Carriage上的倒挂摆在倒挂摆动的解决方案。自1941年本书的外观以来，该解决方案由几个杰出的数学家争论。基于Courant和Robbins的想法的首要正式证明于2014年出版了Byvan Pollkhin .Polekhin还证明了对本体的非周期性解决方案的定理提供了问题，所以运输在线的移动是定期的。在本文中，通过降低运动的规律性等级，我们略微改善了极点，我们证明了一个定期解决的人，如果车厢定期在平面上移动。
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