Sufficient conditions for stability of Euler elasticas

Based on the conjugate point theory in calculus of variations, sufficient conditions on stability of all Euler elasticas for a column clamped at one end and guided at the other are proposed in this paper. For the Euler elasticas, an initial value problem is solved numerically by the Euler iteration. Sufficient conditions are satisfied that Euler elasticas with one half wave are stable and the others with more than one half wave are unstable in post-buckling. As load is smaller than the Euler critical force, it is sufficient theoretically that straight shape is stable. As load exceeds the Euler critical force, it is sufficient theoretically that straight shape is unstable.