A study is made of four algorithms which integrate the rotational equa
tions of motion for rigid linear molecules. They are leapfrog algorith
ms in the sense that the quantities saved between time steps are the o
n-step orientation and the mid-step angular velocity. Thermostatted ve
rsions of the algorithms as well as conventional energy-conserving ver
sions are described. The algorithms are extensively tested in simulati
ons of liquid nitrogen, the aim being to study the effect of increased
time steps on a range of measured properties. The most successful alg
orithm, based on applying a length constraint to the axis vector, show
s remarkable stability and can be used with very large time steps.