Related papers: Non-deterministic dynamics of a mechanical system
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…
We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and…
In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the inclusion of irreversible phenomena in both discrete and…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters. Indeed, experiments on sheared elastic bodies have shown that the static friction coefficient depends on…
Fluctuations in systems away from thermal equilibrium have features that have no analog in equilibrium systems. One of such features concerns large rare excursions far from the stable state in the space of dynamical variables. For…
We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…
The dynamics of moving solids with unilateral contacts are often modeled by assuming rigidity, point contacts, and Coulomb friction due to the simplicity of these models. The canonical example of a rigid rod with one endpoint slipping in…
The dynamics of filaments in flow are central to understanding a wide range of biological and soft-matter systems, yet their behavior under time-dependent forcing remains poorly understood. Here, we investigate the long-time dynamics of…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…