In this paper, the dynamic stability analysis of a simply supported beam carrying a sequence of moving masses is investigated. Many applications such as motion of vehicles or trains on bridges, cranes transporting loads along their span, fluid transfer pipe systems and the barrel of different weapons can be represented as a flexible beam carrying moving masses. The periodical traverse of masses...

Measures calculated from unperturbed walking patterns, such as variability measures and maximum Floquet multipliers, are often used to study the stability of walking. However, it is unknown if, and to what extent, these measures correlate to the probability of falling. We studied whether in a simple model of human walking, i.e., a passive dynamic walker, the probability of falling could be pred...

We present an in–depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a s...

We introduce the concept of Floquet topologicalmagnons—amechanismbywhich a synthetic tunableDzyaloshinskii–Moriya interaction (DMI) can be generated in quantummagnets using circularly polarized electric (laser)field. The resulting effect is thatDiracmagnons and nodal-line magnons in two-dimensional and three-dimensional quantummagnets can be tuned tomagnon Chern insulators andWeylmagnons respec...

Dynamical tunneling has been observed in atom optics experiments by two groups. We show that the experimental results are extremely well described by time-periodic Hamiltonians with momentum quantized in units of the atomic recoil. The observed tunneling has a well defined period when only two Floquet states dominate the dynamics. Beat frequencies are observed when three Floquet states dominate...

Lyapunov exponents and direction elds are used to characterize the time-scales and geometry of general linear time-varying (LTV) systems of di erential equations. Lyapunov exponents are already known to correctly characterize the time-scales present in a general LTV system; they reduce to real parts of eigenvalues when computed for linear time-invariant(LTI) systems and real parts of Floquet ex...

We introduce the concept of Floquet topologicalmagnons—amechanismbywhich a synthetic tunableDzyaloshinskii–Moriya interaction (DMI) can be generated in quantummagnets using circularly polarized electric (laser)field. The resulting effect is thatDiracmagnons and nodal-line magnons in two-dimensional and three-dimensional quantummagnets can be tuned tomagnon Chern insulators andWeylmagnons respec...

We show theoretically that periodically driven systems with short range Hubbard interactions offer a feasible platform to experimentally realize fractional Chern insulator states. We exemplify the procedure for both the driven honeycomb and the square lattice, where we derive the effective steady state band structure of the driven system by using the Floquet theory and subsequently study the in...

We define what it means for time translation symmetry to be spontaneously broken in a quantum system and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.

The time-periodic density of a Floquet state of a time-periodic potential does not uniquely determine that potential. A simple example demonstrates this, and the implications are discussed. 2002 Published by Elsevier Science B.V. Ground-state density functional theory (DFT) [1] has been tremendously successful in predicting the electronic structure of atoms, molecules and solids relatively inex...