TITLE:
Linear Stability of Non-Axial Libration Points in the Kite Configuration of First Kind
AUTHORS:
Mehebub Alam, Md. Rafiqul Hassan, Sandeep Suman, Md. Aminul Hassan, Pranav Kumar, Md. Sabir Ahamad, Sahin Sultana
KEYWORDS:
Kite Configuration, Cyclic Kite Configuration, Rotating Frame, Mass Parameter, Axial and Non-Axial Libration Points, Characteristic Roots, Stability Criteria
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.15 No.3,
August
4,
2025
ABSTRACT: This paper deals with the linear stability of non-axial libration points in the kite configuration of first kind. It is to be noted that the kite configuration of the first kind exists for the mass parameter
μ∈]
0,1/3
[
, where
μ
is the ratio of the smallest mass of the kite to the whole mass of the system. To check the linear stability of the libration points, the variational equation was derived in the neighbourhood of the libration points, and then the characteristic equation was formed. If all the roots of the characteristic equation are purely imaginary, then all criteria for stability will be satisfied and hence, the libration points will be stable; otherwise, unstable. For this, the stability criteria given in Equation (15) have been followed, and it was found that
L
4
and
L
5
are stable for
μ=0.10
only and for all values of
μ∈]
0,1/3
[
,
L
j
(
j=1,2,3,6,7,8,9,10,11,12,13
)
are unstable.