Resonant absorption: Transformation of compressive motions into vortical motions

Resonant motions of the three-dimensional elastic pendulum

The three-dimensionalmotion of the elastic pendulum or swinging spring is investigated in this study. The amplitude is assumed to be small, so that the perturbation approach is valid. If the Lagrangian is approximated by keeping terms up to cubic order, the system has three independent constants of motion; it is therefore completely integrable. The linear normal modes are derived, and some spec...

Resonant Motions of the Three - dimensional Elasti PendulumPeter

Direct excitation of resonant torsional Alfvén waves by footpoint motions

The present paper studies the heating of coronal loops by linear resonant Alfvén waves that are excited by the motions of the photospheric footpoints of the magnetic field lines. The analysis is restricted to torsionally polarised footpoint motions in an axially symmetric system so that only torsional Alfvénwaves are excited. For this subclass of footpointmotions, the Alfvén and cusp singularit...

[Motions].

On bifurcations into nonresonant quasi-periodic motions

The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized perturbation procedure which employs mul...