ON A CLASS OF PLANAR GEOMETRICAL CURVES WITH CONSTANT REACTION FORCES ACTING ON PARTICLES MOVING ALONG THEM

摘要

In this paper, we find the dependence of the reaction force N(y) of a curved trough of arbitrary shape described by a function y(x). Based on the extremum condition dN/dx valid for any point of the abscissa axis, we examine the equation N(y, y', y'') = const whose solutions determine the desired class of curves y(x). We obtain an analytic solution of this equations and perform numerical simulations for various values of parameters. Examples of functions y(x) for which N = const are presented.