相关论文: The Diver with a Rotor

An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus,…

Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible,…

Metriplectic dynamics couple a Poisson bracket of the Hamiltonian description with a kind of metric bracket, for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a…

The mechanism of swimming at very low Reynolds number conditions is a topic of interest to biologists and engineering community. We develop a novel kinematic model of a slender flexible swimmer which locomotes in a low Reynolds number…

The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…

Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…

The primary objective of this thesis is to develop a consistent theoretical framework of dissipative hydrodynamics for a relativistic fluid with spin - hereafter referred to as relativistic dissipative spin hydrodynamics. In this framework,…

Using minimal models for low Reynolds number passive and active rotors in a fluid, we characterize the hydrodynamic interactions among rotors and the resulting dynamics of a pair of interacting rotors. This allows us to treat in a common…

To achieve high-dexterity motion planning on floating-base systems, the base dynamics induced by arm motions must be treated carefully. In general, it is a significant challenge to establish a fixed-base frame during tasking due to forces…

Tendon-driven robotic catheters are capable of precise execution of minimally invasive cardiac procedures including ablations and imaging. These procedures require accurate mathematical models of not only the catheter and tendons but also…

A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…

The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…

The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse…

Spin-orbit coupling is often described in the "MacDonald torque" approach which has become the textbook standard. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (1964; Rev. Geophys. 2,…

In a dissipative system the time to reach an attractor is often influenced by the peculiarities of the model and in particular by the strength of the dissipation. In particular, as a dissipative model we consider the spin-orbit problem…

A very simple explicit integrator for the rotational motion of rigid linear molecules is presented which can preserve the rigidity of the molecules without requiring any constraint force. The integrator is time-reversible and symplectic,…

We construct a normal form suited to {\it fast driven systems}. We call so systems including actions ${\rm I}$, angles {$\psi$}, and one fast coordinate $y$, moving under the action of a vector--field $N$ depending only on ${\rm I}$ and $y$…

Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal…

Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point,…

We have investigated kinematic reversibility in a cold atom system under strongly overdamped conditions. In such systems, inertia is negligible, and for noninteracting rigid particles, inverting the external force causes a perfect reversal…