Related papers: Momentum Map and Action-Angle Variables for Nambu …
For a smooth projective unitary representation of a locally convex Lie group G, the projective space of smooth vectors is a locally convex Kaehler manifold. We show that the action of G on this space is weakly Hamiltonian, and lifts to a…
The nonlinear spin dynamics in antiferromagnetic crystals is studied for the magnetic structures similar to that of hematite. For the case when only two magnetization vectors are non-zero and the Hamiltonian has an axial symmetry, a…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
Using the Hamiltonian formulation, we have attempted to obtain the equations of motion of systems with internal angular momentum that are moving with respect to a reference system when subjected to an interaction. This interaction involves…
The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions…
This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (or repeller), which could be seen as the union of compact…
In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct…
This paper presents a non-minimal order dynamics model for many analysis, simulation, and control problems of constrained mechanical systems with switching topology by making use of linear projection operator. The distinct features of this…
We give a detailed discussion about existence and uniqueness of Lu's momentum map. More precisely, we introduce the infinitesimal momentum map, and we study its properties. This allows us to describe the theory of reconstruction of the…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
In this paper, we introduce dynamics factor graphs as a graphical framework to solve dynamics problems and kinodynamic motion planning problems with full consideration of whole-body dynamics and contacts. A factor graph representation of…
We develop a Hamilton-Jacobi-like formulation of Nambu mechanics. The Nambu mechanics, originally proposed by Nambu more than four decades ago, provides a remarkable extension of the standard Hamilton equations of motion in even dimensional…
It is shown that several Hamiltonian systems possessing dynamical or hidden symmetries can be realized within the framework of Nambu's generalized mechanics. Among such systems are the SU(n)-isotropic harmonic oscillator and the…
When the parameter of a map is chosen, at each iteration step, following a certain rule, is called Parametric Perturbation. If the parameters are drawn from a distribution, then this perturbation is called Random Parametric Perturbation.…
The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether's conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this…
Learning human motion based on a time-dependent input signal presents a challenging yet impactful task with various applications. The goal of this task is to generate or estimate human movement that consistently reflects the temporal…
Reduction theorem for Poisson manifolds with Hamiltonian Lie algebroids is presented. The notion of compatibility of a momentum section is introduced to the category of Hamiltonian Lie algebroids over Poisson manifolds. It is shown that a…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
The Moody diagram, a plot of friction factor versus flow rate, is a well-known engineering tool for estimating head loss in pipe flows. It comprises well-defined relationships between friction factor and flow rate over the majority of…
When human participants repeatedly encounter a velocity-dependent force field that distorts their movement trajectories, they adapt their motor behavior to recover straight trajectories. Computational models suggest that adaptation to a…