Abstract:
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.
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