3. Note on Linear Differential Equations in Quaternions

Extract

The generally non-commutative character of quaternion multiplication introduces into the solution even of linear differential equations with constant (quaternion) coefficients, difficulties of a somewhat novel character. To some of these which have presented themselves to me in many investigations, I wish to draw attention in the following note, but want of leisure prevents my attempting at present either to classify the numerous curious forms which may be met with in physical inquiries, even when these lead to mere physical interest, inasmuch as they include the problem of finding two homogeneous strains, such that the vector-sum of their effects on any vector shall represent the effect of one given strain on that vector, while the effect of their successive performance in a given order on any vector shall be equivalent to that of another given strain.