Related papers: Dual Quaternion Variational Integrator for Rigid B…
Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…
This work investigates variational compilation methods for simulating quantum systems with internal SU(2) symmetry. The central component of the research is the application of the Dynamic Mode Decomposition (DMD) method to extrapolate…
We develop a novel approach for the self-consistent solution of coupled sets of Bethe-Salpeter and Schwinger-Dyson equations in QCD. This framework allows us to maintain the axial Ward-Takahashi identities of the theory within advanced…
In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a…
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…
Solving quaternion kinematical differential equations is one of the most significant problems in the automation, navigation, aerospace and aeronautics literatures. Most existing approaches for this problem neither preserve the norm of…
Applications of reinforcement learning (RL) to stabilization problems of real systems are restricted since an agent needs many experiences to learn an optimal policy and may determine dangerous actions during its exploration. If we know a…
This paper proposes a robust dual-quaternion based H-infinity task-space kinematic controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous disturbances, and their influence upon…
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to…
Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. Although direct trajectory optimization is widely applied to solve this problem, inappropriate parameterizations of rigid body dynamics often…
The discrete velocity method (DVM) is a powerful framework for simulating gas flows across continuum to rarefied regimes, yet its efficiency remains limited by existing quadrature rules. Conventional infinite-domain quadratures, such as…
Quaternions provide a unified algebraic and geometric framework for representing three-dimensional rotations without the singularities that afflict Euler-angle parametrisations. This article develops a pedagogical and conceptual analysis of…
We investigate the application of efficient recursive numerical integration strategies to models in lattice gauge theory from quantum field theory. Given the coupling structure of the physics problems and the group structure within lattice…
Various dynamical engineering systems involve purely nonlinear stiffness that lacks linear properties even under the assumption of small displacements. The most common is the cubic nonlinearity that may stem from either geometric or…
We present a principled method for dynamic simulation of rigid bodies in intermittent contact with each other where the contact is assumed to be a non-convex contact patch that can be modeled as a union of convex patches. The prevalent…
An asynchronous, variational method for simulating elastica in complex contact and impact scenarios is developed. Asynchronous Variational Integrators (AVIs) are extended to handle contact forces by associating different time steps to…
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…
Imitation learning techniques have been used as a way to transfer skills to robots. Among them, dynamic movement primitives (DMPs) have been widely exploited as an effective and an efficient technique to learn and reproduce complex discrete…
This study examines several techniques to improve the efficiency of the linearized multireference driven similarity renormalization group truncated to one- and two-body operators [MR-LDSRG(2)]. We propose a sequential MR-LDSRG(2)…
Deep learning has shown promise in improving computing efficiency while ensuring modeling accuracy in fluid-structure interaction (FSI) analysis. However, its current capabilities are limited when it comes to constructing multi-object…