相关论文: Dynamics of Mobile Manipulators using Dual Quatern…

This paper introduces a general framework for solving constrained convex quaternion optimization problems in the quaternion domain. To soundly derive these new results, the proposed approach leverages the recently developed generalized…

In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…

In this paper, the dynamic modeling of a seven linked humanoid robot, is accurately developed, in the three dimensional space using the Newton-Euler formalism. The aim of this study is to provide a clear and a systematic approach so that…

The criterion of differentiability of functions of quaternion variable is used as the basis of some algebraic field theory. Its necessary consequences are free Maxwell and Yang-Mills equations. The differentiability equations may be…

We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with…

In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily…

We present an equation generator algorithm that utilizes second-quantized operators in normal order with respect to a correlated or non-correlated reference and the corresponding Wick theorem. The algorithm proposed here, written with…

By introducing auxiliary fields, which by their quantum numbers vanish in perturbation theory, we relate the dynamical perturbation theory of Pagels and Stokar and a successful gauged nonlocal constituent quark model to $U(N)$ gauge theory…

This paper presents solutions to the following two common quaternion attitude estimation problems: (i) estimation of attitude using measurement of two reference vectors, and (ii) estimation of attitude using rate measurement and measurement…

The dual consistency is an important issue in developing stable DWR error estimation towards the goal-oriented mesh adaptivity. In this paper, such an issue is studied in depth based on a Newton-GMG framework for the steady Euler equations.…

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a new numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner…

This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…

This paper showed that Poisson brackets in quaternion variables can be obtained directly from canonical Poisson brackets on cotangent bundle of $SE(3)$ (or $SO(3)$) endowed by canonical symplectic geometry. Quaternion parameters in our case…

We extract the square root of the Minkowski metric using Dirac/Clifford matrices. The resulting $4\times 4$ operator $d{\bf S}$ that represents the square root, can be used to transform four vectors between relatively moving observers. This…

In a dual weighted residual method based on the finite element framework, the Galerkin orthogonality is an issue that prevents solving the dual equation in the same space as the one for the primal equation. In the literature, there have…

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a…

Intrinsically stable magnetic levitation between superconductors and permanent magnets can be exploited in a variety of applications of great technical interest in the field of transportation (rail transportation), energy (flywheels) and…

We have introduced a new method for computing gravitational-wave emission from nonspinning binaries which systematically unifies the various integrals arising in the Fourier expansions of post-Newtonian dynamics, providing a simple,…

This paper investigates the tracking problem of a smooth coordinate-invariant trajectory using dual quaternion algebra. The proposed architecture consists of a cascade structure in which the outer-loop MPC performs real-time smoothing of…

We propose a new primal-dual algorithmic framework for a prototypical constrained convex optimization template. The algorithmic instances of our framework are universal since they can automatically adapt to the unknown Holder continuity…