Abstract

CONDORI U, Nestor Rodrigo  and  SANJINES CASTEDO, Diego. Stability zone estimation in an elastic pendulum model. Revista Boliviana de Física [online]. 2019, vol.34, n.34, pp.19-32. ISSN 1562-3823.

Abstract We investigate the elastic pendulum dynamical system with two degrees of freedom (radial and angular) through the Lagrangian formalism which yields a system of two coupled non-linear differ-ential equations. By projecting the radial coordinate, we obtain a Hill equation with a time-periodic coefficient modelled by a piecewise constant function. A stability diagram for the characteristic pa-rameters of the system is then calculated by means of a criterion based on the trace of the evolution matrix without invoking the small oscillation approximation. The numerical solution of the system equations for the chosen parameters verifies the precision of the calculated stability diagram and a reasonably good agreement is found. For small oscillations we obtain the known results of the Mathieu equation and its corresponding stability diagram (Strutt diagram). We finally discuss some interesting perspectives.

Keywords : Nonlinear dynamics; Lagrangian and Hamiltonian mechanics; Energy conservation.

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