Open AccessParametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit
Author(s) -
José Laudelino de Menezes Neto,
Gerson Cruz Araujo,
Yocelyn Pérez Rothen,
Cláudio Vidal
Publication year - 2022
Publication title -
journal of geometric mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.511
H-Index - 17
eISSN - 1941-4897
pISSN - 1941-4889
DOI - 10.3934/jgm.2021031
Subject(s) - pendulum , orbit (dynamics) , orbital eccentricity , elliptic orbit , eccentricity (behavior) , physics , mathematics , hamiltonian (control theory) , mathematical analysis , classical mechanics , planet , quantum mechanics , law , political science , engineering , aerospace engineering , mathematical optimization , astrophysics
We consider the planar double pendulum where its center of mass is attached in an elliptic orbit. We consider the case where the rods of the pendulum have variable length, varying according to the radius vector of the elliptic orbit. We make an Hamiltonian view of the problem, find four linearly stable equilibrium positions and construct the boundary curves of the stability/instability regions in the space of the parameters associated with the pendulum length and the eccentricity of the orbit.