相关论文: Singularity-Free Lie Group Integration and Geometr…

The dynamics simulation of multibody systems (MBS) using spatial velocities (non-holonomic velocities) requires time integration of the dynamics equations together with the kinematic reconstruction equations (relating time derivatives of…

After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this…

Many-body localization (MBL), characterized by the absence of thermalization and the violation of conventional thermodynamics, has elicited much interest both as a fundamental physical phenomenon and for practical applications in quantum…

Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two…

Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS) while at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows for use of…

Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such…

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…

Many-body localization (MBL) is understood theoretically through the existence of an extensive number of local integrals of motion (LIOMs). These conserved quantities are related to the microscopic quantum degrees of freedom that are…

Parallel manipulators, also called parallel kinematics machines (PKM), enable robotic solutions for highly dynamic handling and machining applications. The safe and accurate design and control necessitates high-fidelity dynamics models.…

We compare three approaches to posing the index 3 set of differential algebraic equations (DAEs) associated with the constrained multibody dynamics problem formulated in absolute coordinates. The first approach works directly with the…

Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body localized (MBL) systems are characterized by extensively many local integrals of motion…

In many applications, one encounters signals that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are examples of ubiquitous mathematical objects that have a non Euclidean structure. The application of…

Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on…

Rigid body dynamics on the rotation group have typically been represented in terms of rotation matrices, unit quaternions, or local coordinates, such as Euler angles. Due to the coordinate singularities associated with local coordinate…

We present a symmetry-based framework for equilibrium statistical mechanics that formulates a single Lie group combining conventional spacetime symmetries with a recently identified phase-space gauge-shifting invariance [Muller et al.,…

We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…

We review the current (as of Fall 2016) status of the studies on the emergent integrability in many-body localized models. We start by explaining how the phenomenology of fully many-body localized systems can be recovered if one assumes the…

We study many-body localization (MBL) and delocalization from the perspective of integrals of motion (IOMs). MBL can be understood phenomenologically through the existence of macroscopically many localized IOMs. However, IOMs exist for all…

An effective paradigm for simulating the dynamics of robots that locomote and manipulate is multi-rigid body simulation with rigid contact. This paradigm provides reasonable tradeoffs between accuracy, running time, and simplicity of…

In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multi-body systems. Although the motion of multi-body systems is considered to be a well-studied problem and…