相关论文: A 'User-Friendly' Approach to the Dynamical Equati…

We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…

In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…

In this paper, we present a collection of infinite-dimensional systems with nonholonomic constraints. In finite dimensions the two essentially different types of dynamics, nonholonomic or vakonomic ones, are known to be obtained by taking…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution…

We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and…

In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…

We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…

We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…

Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…

We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…

A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…

We use covariant methods to analyse the nonlinear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous…

We consider nonholonomic systems with collisions and propose a concept of weak solutions to Lagrange-d'Alembert equations. In the light of this concept we describe dynamics of the collisions. Several applications have been investigated.…

Nonlinear control-affine systems with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems. This…

We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on the square lattice. The fields are associated to the vertices and an equation Q(x_1,x_2,x_3,x_4)=0 relates four fields at one quad. Integrability of…

The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…

We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic…

Multibody systems usually give rise to complex nonlinear dynamics, and the bicycle is not an exception. Even a simple model as the Two-Mass-Skate presents a long expression of the kinetic energy, making difficult to write explicitly the…