  The effects of finite amplitudes on the transverse oscillations of a
quiescent prominence represented by a magnetic rope are investigated in terms
of the model proposed by Kolotkov et al. 2016. We consider a weakly nonlinear
case governed by a quadratic nonlinearity, and also analyse the fully nonlinear
equations of motion. We treat the prominence as a massive line current located
above the photosphere and interacting with the magnetised dipped environment
via the Lorentz force. In this concept the magnetic dip is produced by two
external current sources located at the photosphere. Finite amplitude
horizontal and vertical oscillations are found to be strongly coupled between
each other. The coupling is more efficient for larger amplitudes and smaller
attack angles between the direction of the driver and the horizontal axis.
Spatial structure of oscillations is represented by Lissajous-like curves with
the limit cycle of a hourglass shape, appearing in the resonant case, when the
frequency of the vertical mode is twice the horizontal mode frequency. A
metastable equilibrium of the prominence is revealed, which is stable for small
amplitude displacements, and becomes horizontally unstable, when the amplitude
exceeds a threshold value. The maximum oscillation amplitudes are also
analytically derived and analysed. Typical oscillation periods are determined
by the oscillation amplitude, prominence current, its mass and position above
the photosphere, and the parameters of the magnetic dip. The main new effects
of the finite amplitude are the coupling of the horizontally and vertically
polarised transverse oscillations (i.e. the lack of a simple, elliptically
polarised regime) and the presence of metastable equilibria of prominences.
