EXPONENTIAL SOLUTION OF A DIFFERENTIAL EQUATION BETWEEN OPERATORS

Authors : H. Luna-garcia, Luz Maria Garcia-cruz

Pages : 118-125

Doi:10.36753/mathenot.421229

View : 13 | Download : 12

Publication Date : 2015-05-15

Article Type : Research

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.
Keywords : Exponential of a matrix, Lie groups, Frenet-Serret equation