Before revision: Then, the solution of the original equation is: Now, we will use the boundary conditions: No moment at Fixed at From the second B.C., we get that the critical length in which a vertical column will buckle under its own weight is: Using , the first zero of the Bessel function of the first kind of order , can be approximated to The column under its own weight was considered by Euler in three famous papers (1778a, 1778b, 1778c)Euler, L. (1778a) Determinatio onerum, quae columnae gestare valent, Acta Academiae Scientiarum Petropolitanae, Vol.
After revision: :Euler's mistakeThen, the solution of the original equation is: Now, we will use the boundary conditions: No moment at Fixed at From the second B.C., we get that the critical length in which a vertical column will buckle under its own weight is: Using , the first zero of the Bessel function of the first kind of order , can be approximated to The column under its own weight was considered by Euler in three famous papers (1778a, 1778b, 1778c)Euler, L. (1778a) Determinatio onerum, quae columnae gestare valent, Acta Academiae Scientiarum Petropolitanae, Vol.