Abstract: Post-buckling configuration of a slender rod constrained in a cylinder is described with Euler-Rodrigues parameters.Corresponding energy function is obtained.Nonlinear differential equilibrium equation and contact force are established through the energy function.The problem is solved successfully with finite element method.To verify the formulations and solutions,comparisons with existing data or solutions are made.Numerical results revealed conversion process from sinusoidal buckling to helix buckling.Possibility of mode changing in post-buckling process is verified.

Key words: Euler-Rodrigues parameter, inclined cylinder, helix buckling, mode transition, finite element method