EXPONENTIAL SOLUTION OF A DIFFERENTIAL EQUATION BETWEEN OPERATORS

Year 2015, , 118 - 125, 15.05.2015

H. Luna-garcia Luz Maria Garcia-cruz

https://doi.org/10.36753/mathenot.421229

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

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