74 citations · 574 across the 42 of their papers we have counts for
5 papers · 1 filter
Quaternion Solution for the Rock'n'roller: Box Orbits, Loop Orbits and Recession
Peter Lynch, Miguel D Bustamante
We consider two types of trajectories found in a wide range of mechanical systems, viz. box orbits and loop orbits. We elucidate the dynamics of these orbits in the simple context…
Resonance clustering in wave turbulent regimes: Integrable dynamics
Elena Kartashova, Miguel D. Bustamante
Two fundamental facts of the modern wave turbulence theory are 1) existence of power energy spectra in -space, and 2) existence of "gaps" in this spectra corresponding to the re…
Precession and Recession of the Rock'n'roller
Peter Lynch, Miguel D. Bustamante
We study the dynamics of a spherical rigid body that rocks and rolls on a plane under the effect of gravity. The distribution of mass is non-uniform and the centre of mass does not…
Effect of the dynamical phases on the nonlinear amplitudes' evolution
Miguel D. Bustamante, Elena Kartashova
In this Letter we show how the nonlinear evolution of a resonant triad depends on the special combination of the modes' phases chosen according to the resonance conditions. This ph…
Dynamics of nonlinear resonances in Hamiltonian systems
Miguel D. Bustamante, Elena Kartashova
It is well known that the dynamics of a Hamiltonian system depends crucially on whether or not it possesses nonlinear resonances. In the generic case, the set of nonlinear resonanc…