An in-house simulation program, based on the mathematical model of a motor formulated as the Lagrange function
, which uses array dependencies of the magnetic flux (Fig.
According to this idea, the following Lagrange function
According to the Lagrange multipliers method, Lagrange function
is as follows:
 proposed the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function
. However, Sheikh et al.
We construct the Lagrange function
according to the optimization problem
In order to ensure the smoothness of the pendular motion of the tethered system during orbital transfer, the Lagrange function
[mathematical expression not reproducible] is adopted.
According to Lagrange multiplier method, the first-order derivatives of the Lagrange function
should equal zero when the minimum of the cost function is got,
If there exist nonnegative real-valued Lagrange function
multipliers [u.sub.j] for j = 1, 2, ..., m defined on [0, 1] such that
The original problem is transformed into dual problem, and the Lagrange function
is introduced to solve this problem.
The above approach allows you to avoid decomposition of single dynamic system, and to obtain initial state equation energetic exclusively on a single approach, enhanced by constructing Lagrange function
We apply Lagrange multiplier to construct the Lagrange function
including objective function and constraint function simultaneously.
L(x, [gamma]) = [c.sup.T] x + [gamma]h (x) is Lagrange function
. [lambda] is termed as Lagrange multiplier.