  We analyse the forces that control the dynamic evolution of a flux rope
eruption in a three-dimensional (3D) radiative magnetohydrodynamic (RMHD)
simulation. The confined eruption of the flux rope gives rise to a C8.5 flare.
The flux rope rises slowly with an almost constant velocity of a few km/s in
the early stage, when the gravity and Lorentz force are nearly counterbalanced.
After the flux rope rises to the height at which the decay index of the
external poloidal field satisfies the torus instability criterion, the
significantly enhanced Lorentz force breaks the force balance and drives rapid
acceleration of the flux rope. Fast magnetic reconnection is immediately
induced within the current sheet under the erupting flux rope, which provides a
strong positive feedback to the eruption. The eruption is eventually confined
due to the tension force from the strong external toroidal field. Our results
suggest that the gravity of plasma plays an important role in sustaining the
quasi-static evolution of the pre-eruptive flux rope. The Lorentz force, which
is contributed from both the ideal magnetohydrodynamic (MHD) instability and
magnetic reconnection, dominates the dynamic evolution during the eruption
process.
