We study the dynamics of a vortex in superfluid He4. This is carried o
ut by deriving the effective Lagrangian for the center of the vortex b
y starting with the time-dependent Ginzburg-Landau formalism. From the
resultant equation of motion for a vortex, rye arrive at a novel aspe
ct for the Magnus force which has long been known in fluid dynamics. T
his force has a geometric origin and is expected to occur in other for
m Of condensates such as vortex excitations for quantum Hall fluids or
ferromagnets, We also consider the force of non geometric origin, the
pinning force coming from the impurity.