相关论文: Extracting Dynamical Frequencies from Invariants o…
In non-degenerate integrable Hamiltonian systems, invariant tori can be parameterized equivalently by action variables or by their fundamental frequencies. We introduce an invariant-flow formulation for extracting fundamental frequencies of…
Understanding the dynamics of generic 3D scenes is fundamentally challenging in computer vision, essential in enhancing applications related to scene reconstruction, motion tracking, and avatar creation. In this work, we address the task as…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
Some mechanical systems, that are modeled to have inelastic collisions, nonetheless possess energy-conserving intermittent-contact solutions, known as collisionless solutions. Such a solution, representing a persistent hopping or walking…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
In this paper is proposed the method of the identification of complex dynamic systems. Method can be used for the identification of linear and nonlinear complex dynamic systems for the determined or stochastic signals at the inputs and the…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
We consider learning underlying laws of dynamical systems governed by ordinary differential equations (ODE). A key challenge is how to discover intrinsic dynamics across multiple environments while circumventing environment-specific…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
This paper begins with a dynamical model that was obtained by applying a machine learning technique (FJet) to time-series data; this dynamical model is then analyzed with Lie symmetry techniques to obtain constants of motion. This analysis…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
We present an efficient algorithm for motion planning and control of a robot system with a high number of degrees-of-freedom. These include high-DOF soft robots or an articulated robot interacting with a deformable environment. Our approach…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned…
The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The natural frequencies and damping behaviour can be easily and quickly detected from a Bode diagram. The modal…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
We develop a method, based on Darboux' and Liouville's works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements' form. We apply it to…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…