相关论文: Momentum Map and Action-Angle Variables for Nambu …

A basic shallow water system with variable topography is analyzed from the point of view of a Lagrangian derivation of momentum, energy, and pseudomomentum balances. A two-dimensional action and associated momentum equation are derived. The…

In this paper we study the reduction of a nonholonomic system by a group of symmetries in two steps. Using the so-called 'vertical-symmetry' condition, we first perform a 'compression' of the nonholonomic system leading to an almost…

A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…

The solution with respect to the reduced action of the one-dimensional stationary quantum Hamilton-Jacobi equation is well known in the literature. The extension to higher dimensions in the separated variable case was proposed in…

The computational Projective Dynamics method is used to analyze simulations of magnetization reversal in nanoscale magnetic pillars. It is shown that this method can be used to determine the magnetizations corresponding to the metastable…

The minimum action method (MAM) is to calculate the most probable transition path in randomly perturbed stochastic dynamics, based on the idea of action minimization in the path space. The accuracy of the numerical path between different…

Taking as a model the fact that Heisenberg's matrix mechanics was derived from Hamiltonian mechanics using the correspondence principle, we explore a class of dynamical systems involving discrete variables, with Nambu mechanics as the…

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

We consider how the reduced dynamics of an open quantum system coupled to an environment admits the Poincar\'e symmetry. The reduced dynamics is described by a dynamical map, which is given by tracing out the environment from the total…

This paper revisits momentum in the context of min-max optimization. Momentum is a celebrated mechanism for accelerating gradient dynamics in settings like convex minimization, but its direct use in min-max optimization makes gradient…

Considering a Hamiltonian Dynamical System describing the motion of charged particle in a Tokamak or a Stellarator, we build a change of coordinates to reduce its dimension. This change of coordinates is in fact an intricate succession of…

This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket…

Modern optimal control theory involves adjoining the already known equations of motion of a dynamic system to the objective function using dynamic costates; this is done in order to constrain the optimal control solutions to satisfy the…

We present a novel approach for studying the global dynamics of a vibro-impact pair, that is, a ball moving in a harmonically forced capsule. Motivated by a specific context of vibro-impact energy harvesting, we develop the method with…

This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inverse-kinematics problems. We…

We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid…

In his pioneering paper [Phys. Rev. E 7, 2405 (1973)], Nambu proposed the idea of multiple Hamiltonian systems. The explicit example examined there is equivalent to the so(3) Lie-Poisson system, which represents noncanonical Hamiltonian…