Equilibrium and Stability of Elastic Rod Constrained to Cylinder
Liu Yanzhu(1),Xue Yun(2)
(1 Shanghai Jiaotong University, Shanghai 200030) (2 Shanghai Institute of Technology, Shanghai 200233)

Abstrac: The equilibrium and stability of an elastic rod with circular cross section under the constraint of a cylinder is discussed. The differential equations of equilibrium of the constrained rod are established taking Euler angles as variables to describe the attitude of the cross section. The analytical expres sions of constraint force, internal force on cross section, and flexibility of the rod are obtained via the first integrals. The existence conditions of helical equilibrium are discussed as a special configuration of the rod. The stability of the helical equilibrium is analyzed with phase plane method, and an analytic al criterion of stability is revealed.
Keywords: thin elastic rod, cylinder constraint, stability, phase plane method.