DISCUSSION ON THE STABILITY OF EULER'S POLE

The critical axial pressures of an Euler's pole in some constraint conditions are well known. According to the derivation, the Euler's staight pole might be in a curved static state and lose stability only if the axial pressure is equal to some integer multiple of the critical axial pressure value. When the pressure is between two integer multiples of the critical value, the pole might not be in a curved static state. In other words, it will remain in a straight state and will not lose stability. This is obviously not consistent with the reality. The problem is discussed in this paper by using the exact formula of the pole's curvature. The reason why the pull-pole will not lose stability is explained. Meanwhile, the variation of the pole's deflection curve with the increase of the axial pressure is discussed.