A motion of connected pendulums

A motion of two identical pendulums connected by a linear elastic spring with an arbitrary stiffness is investigated. The system moves in an homogeneous gravitational field in a fixed vertical plane. The paper mainly studies the linear orbital stability of a periodic motion for which the pendulums accomplish identical oscillations with an arbitrary amplitude. This is one of two types of nonlinear normal oscillations. Perturbational equations depend on two parameters, the first one specifies the spring stiffness, and the second one defines the oscillation amplitude. Domains of stability and instability in a plane of these parameters are obtained.
Previously [1, 2] the problem of arbitrary linear and nonlinear oscillations of a small amplitude in a case of a small spring stiffness was investigated.