Geomagnetic Attitude Control of Satellites Using Generalized Multiple Scales

Abstract

The dynamics of satellites utilizing geomagnetic attitude control with a specific control law are analyzed. Two types of satellites are considered, namely single spin asymmetric satellites and dual spin satellites. Stability criteria and approximate description of the motion of the satellites are obtained in a parametric form (analytical) using the Generalized Multiple Scales (GMS) method. By means of this method, the rapid and slow parts of the dynamics are systematically separated, leading to insight into the nature of the system. Finally, a good agreement between the approximate analytical and numerical solutions is demonstrated.

Analysis of non-dimensional forms of singular perturbation structures for hypersonic vehicles

“…3. It is observed that the equation in (15) does not involve the constant parameter and it may be better to retain the parameter with the equation itself instead of absorbing into the parameter set in (14) as done in Structure 2 described next.…”

“…(1) results in a singular perturbation structure (15) where the parameter responsible for singular perturbation structure is associated (i.e., multiplying the derivative) not only with the non-dimensional radial distancer and flight path angle as obtained by Calise et al [6], but also with the non-dimensional , , and . Thus, there are five fast variables and two slow variables.…”

“…The reason for introducing a second small parameter 2 is to show the multiple-scale character of the dynamics [15]. However, to continue with multiple scales will lead to unnecessary lengthy analysis and also to compare with the other non-dimensional Forms 1 and 2, we will replace 2 with under suitable choice of 0 = 1 as shown below.…”

“…The second small parameter 2 shows the multiple-scale character of the dynamics [15]. We wish to present the analysis for this form.…”