rolling ball differential equation on plane

Hello,

Is it possible to solve the following ordinary differential equation ?

R'(t)=R(t)*[(g'_1(t),g'_2(t),0)^(0,0,1)]_X

where t : time
and ^ is the exterior product
and []_X is the anisymetric matrix associated with the vector in R^3
(g'_1(t),g'_2(t),0)^(0,0,1)

g_1(t) and g_2(t) are for example polynomial fonction of time.


Thanks

.