EXPONENTIAL SOLUTION OF A DIFFERENTIAL EQUATION BETWEEN OPERATORS

Abstract

In this paper we obtain an authentically exponential solution to the differential equation dY (t)/ dt = A(t)Y (t), where Y (t) and A(t) are linear operators with the initial condition Y (0) = I, and I is the identity operator. Then, the solution was applied to calculate the vector triad: tangent, normal and binormal in terms of the arc length of a curve.