Abstract
A linear stability analysis of the coplanar, rigid motion of 4 equal masses about their centre of mass is presented. We consider cases where particles are located at (A) the centre of a square, (B) the vertices and centroid of an equilateral triangle and (C) designated points on a line. The variational equations are analysed in the rotating frame. These equations decompose into invariant subspaces of perturbation evolution in the orbital plane and in the normal direction. All the three cases, A, B and C are linearly unstable. It is worth pointing out that, for cases A and B, perturbations normal to the orbital plane have amplitudes which grow as a power of time t.
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© 1999 Springer Science+Business Media Dordrecht
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Gomatam, J., Steves, B.A., Roy, A.E. (1999). Some Equal Mass Four-Body Equilibrium Configurations: Linear Stability Analysis. In: Steves, B.A., Roy, A.E. (eds) The Dynamics of Small Bodies in the Solar System. NATO ASI Series, vol 522. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9221-5_36
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DOI: https://doi.org/10.1007/978-94-015-9221-5_36
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5133-2
Online ISBN: 978-94-015-9221-5
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