相关论文: The dynamical rigid body with memory
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it was noted by many authors, the analogous result is true for a…
In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
We give a nontechnical description of the behaviour of dynamical systems governed by two distinct time scales. We discuss in particular memory effects, such as bifurcation delay and hysteresis, and comment the scaling behaviour of…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Soft materials are not only highly deformable but they also possess rich and diverse body dynamics. Soft body dynamics exhibit a variety of properties, including nonlinearity, elasticity, and potentially infinitely many degrees of freedom.…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
We review recent work on systems with multiple interacting-particles having the dynamical feature of stochastic resetting. The interplay of time scales related to inter-particle interactions and resetting leads to a rich behavior, both…
In this note we study the structure and the behavior of inarticulate robots. We introduce a robot that moves by successive revolvings. The robot's structure is analyzed, simulated and discussed in detail.