"Comments on a Paper of Idrisi, Ullah and Sikkandhar (Effect of Perturbations in Coriolis and Centrifugal Forces on Libration Points in the Restricted Six-Body Problem: JAS (2021) 68:4-25)".

In a recent paper, Idrisi, Ullah and Sikkandhar [[1]] considered some aspects of the Restricted Six-Body Problem. Besides, as is known from elemental Mechanics courses (see e.g. [[18], p. 55]), the Coriolis force (per unit mass) I C i with angular velocity vector I i perpendicular to the plane I O i I x i I y i is HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>C</mi><mo>=</mo><mo>-</mo><mn>2</mn><mi> </mi><mo>×</mo><mi>v</mi><mo>=</mo><mo>-</mo><mn>2</mn><mi> </mi><mo stretchy="false">(</mo><mo>-</mo><mover accent="true"><mrow><mi>y</mi></mrow><mo> </mo></mover><mo>,</mo><mover accent="true"><mrow><mi>x</mi></mrow><mo> </mo></mover><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo><mo>,</mo></mrow></math> ht Graph and the centrifugal force I Z i is HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Z</mi><mo>=</mo><mo>-</mo><mi> </mi><mo>×</mo><mo stretchy="false">(</mo><mi> </mi><mo>×</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mrow><mi> </mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo><mn>.</mn></mrow></math> ht Graph Hence, if they put in the Coriolis term HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi> </mi></mrow><mrow><mi>'</mi></mrow></msup><mo>=</mo><mi> </mi><mi> </mi></math> ht , the corresponding term in the centrifugal force would be HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi> </mi></mrow><mrow><mi>'</mi><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi> </mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi> </mi></mrow><mrow><mn>2</mn></mrow></msup></math> ht , that is, in their paper there should be I i = I i SP 2 sp , which means that I i is determined by I i , and cannot be a different parameter. [Extracted from the article]