  In this article, sets of analytical formulas for calculation of nine
components of magnetic stiffness of corresponding force arising between two
current-carrying circular filaments arbitrarily oriented in the space are
derived by using Babic's method and the method of mutual inductance
(Kalantarov-Zeitlin's method). Formulas are presented through integral
expressions, whose kernel function is expressed in terms of the elliptic
integrals of the first and second kinds. Also, we obtained an additional set of
expressions for calculation of components of magnetic stiffness by means of
differentiation of Grover's formula of the mutual inductance between two
circular filaments with respect to appropriate coordinates. The derived sets of
formulas were mutually validated and results of calculation of components of
magnetic stiffness agree well to each other.
