<Dd> R new = exp ⁡ ((ω (R old)) × d t) R old (\ displaystyle (\ boldsymbol (R)) _ (\ text (new)) = \ exp \ left (\ left ((\ boldsymbol (\ omega)) \ left ((\ boldsymbol (R)) _ (\ text (old)) \ right) \ right) _ (\ times) dt \ right) (\ boldsymbol (R)) _ (\ text (old))) </Dd> <P> for the skew - symmetric matrix (ω). The errors induced by finite time steps tend to increase the rotational kinetic energy: </P> <Dl> <Dd> E (R) = ω (R) ⋅ L 2 (\ displaystyle E \ left ((\ boldsymbol (R)) \ right) = (\ boldsymbol (\ omega)) \ left ((\ boldsymbol (R)) \ right) \ cdot (\ frac (\ boldsymbol (L)) (2))) </Dd> </Dl> <Dd> E (R) = ω (R) ⋅ L 2 (\ displaystyle E \ left ((\ boldsymbol (R)) \ right) = (\ boldsymbol (\ omega)) \ left ((\ boldsymbol (R)) \ right) \ cdot (\ frac (\ boldsymbol (L)) (2))) </Dd>

Motions of the earth rotation revolution and precession