This article is cited in 7 papers

Parametric Stability of a Pendulum with Variable Length in an Elliptic Orbit

José Laudelino de Menezes Neto^a, Hildeberto E. Cabral<sup>b

a</sup> Departamento de Ciências Exatas, Universidade Federal da Paraíba, 58297-000 Rio Tinto, Brazil
^b Departamento de Matemática, Universidade Federal de Pernambuco, 50670-901 Recife, Brazil

Abstract: We study the dynamics of a simple pendulum attached to the center of mass of a satellite in an elliptic orbit. We consider the case where the pendulum lies in the orbital plane of the satellite. We find two linearly stable equilibrium positions for the Hamiltonian system describing the problem and study their parametric stability by constructing the boundary curves of the stability/instability regions.

Keywords: pendulum, parametric stability.

MSC: 70F15, 34D20, 70H14

Received: 14.12.2019
Accepted: 15.05.2020

Language: English

DOI: 10.1134/S1560354720040012

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