Related papers: The dynamical rigid body with memory
A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…
We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate $N=\mathcal{O}(10^6)$ particles or more. As a first application we consider a dense…
Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes,…
In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on…
We present a complete analysis of the linearised dynamics of active solids with orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include the possibility of stable active…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension $n$. Our aim is to present some analytical methods and to discuss…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
In many real-world settings, image observations of freely rotating 3D rigid bodies, such as satellites, may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of…
We investigate the dynamics of a deterministic self-propelled particle endowed with coherent memory. We evidence experimentally and numerically that it exhibits several stable free states. The system is composed of a self-propelled drop…
The idea of dissipative mechanical system with delay is proposed. The paper studies the phenomenon of dissipation with delay for Euler-Poincare systems on Lie algebras or equivalently, for Lie-Poisson systems on the duals of Lie algebras.…
It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…
Discussed is a model of the two-dimensional affinely-rigid body with the double dynamical isotropy. We investigate the systems with potential energies for which the variables can be separated. The special stress is laid on the model of the…
Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular…
In this paper, we propose to estimate the forward dynamics equations of mechanical systems by learning a model of the inverse dynamics and estimating individual dynamics components from it. We revisit the classical formulation of rigid body…
A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be…