On the Global Geometric Structure of the Dynamics of the Elastic Pendulum
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摘要: We approach the planar elastic pendulum as a singular perturbation of to show that its dynamics are governed by global two-dimensional invariant manifolds motion. One is nonlinear and carries purely slow periodic oscillations. The other one, on hand, linear fast radial For sufficiently small coupling between angular degrees freedom, both orbitally stable up energy levels exceeding unstable equilibrium system. fixed value coupling, manifold bifurcates transversely create oscillations exhibiting transfer. Poincare sections iso-energetic reveal only motions near separatrix emanating from region exhibit
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