样式: 排序: IF: - GO 导出 标记为已读
-
The evolution equation: An application of groupoids to material evolution Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-24 Víctor Manuel Jiménez, Manuel de León
The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the material point and its characteristic foliations, which permits us to define the evolution equation. We also discuss phenomena like remodeling and aging.
-
Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-24 Brennan McCann, Morad Nazari
Presented herein are a class of methodologies for conducting constrained motion analysis of rigid bodies within the Udwadia-Kalaba (U-K) formulation. The U-K formulation, primarily devised for systems of particles, is advanced to rigid body dynamics in the geometric mechanics framework and a novel development of U-K formulation for use on nonlinear manifolds, namely the special Euclidean group \begin{document}$
-
Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-12 André Marques, Fátima Silva Leite
This paper is devoted to rolling motions of one manifold over another of equal dimension, subject to the nonholonomic constraints of no-slip and no-twist, assuming that these motions occur inside a pseudo-Euclidean space. We first introduce a definition of rolling map adjusted to this situation, which generalizes the classical definition of Sharpe [26] for submanifolds of an Euclidean space. We also
-
Modeling student engagement using optimal control theory Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-12 Debra Lewis
Student engagement in learning a prescribed body of knowledge can be modeled using optimal control theory, with a scalar state variable representing mastery, or self-perceived mastery, of the material and control representing the instantaneous cognitive effort devoted to the learning task. The relevant costs include emotional and external penalties for incomplete mastery, reduced availability of cognitive
-
Parametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-12 José Laudelino de Menezes Neto, Gerson Cruz Araujo, Yocelyn Pérez Rothen, Claudio Vidal
We consider the planar double pendulum where its center of mass is attached in an elliptic orbit. We consider the case where the rods of the pendulum have variable length, varying according to the radius vector of the elliptic orbit. We make an Hamiltonian view of the problem, find four linearly stable equilibrium positions and construct the boundary curves of the stability/instability regions in the
-
Constrained systems, generalized Hamilton-Jacobi actions, and quantization Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Alberto S. Cattaneo,Pavel Mnev,Konstantin Wernli
Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In the classical theory, systems with infinite-dimensional targets are considered as well (this then encompasses also higher-dimensional field theories in the hamiltonian formalism). The properties of the Hamilton–Jacobi (HJ) action are described in details and several examples are explicitly computed
-
On embedding of subcartesian differential space and application Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Qianqian Xia
Consider a locally compact, second countable and connected subcartesian differential space with finite structural dimension. We prove that it admits embedding into a Euclidean space. The Whitney embedding theorem for smooth manifolds can be treated as a corollary of embedding for subcartesian differential space. As applications of our embedding theorem, we show that both smooth generalized distributions
-
Modular class of Lie $ \infty $-algebroids and adjoint representations Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Raquel Caseiro,Camille Laurent-Gengoux
We study the modular class of \begin{document}$ Q $\end{document}-manifolds, and in particular of negatively graded Lie \begin{document}$ \infty $\end{document}-algebroid. We show the equivalence of several descriptions of those classes, that it matches the classes introduced by various authors and that the notion is homotopy invariant. In the process, the adjoint and coadjoint actions up to homotopy
-
Efficient geometric linearization of moving-base rigid robot dynamics Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Martijn Bos,Silvio Traversaro,Daniele Pucci,Alessandro Saccon
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state estimation. Contrary to the case of fixed based manipulators with prismatic or revolute joints, the state space of moving-base robotic systems such as humanoids, quadruped
-
Infinite lifting of an action of symplectomorphism group on the set of bi-Lagrangian structures Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Bertuel Tangue Ndawa
We consider a smooth \begin{document}$ 2n $\end{document}-manifold \begin{document}$ M $\end{document} endowed with a bi-Lagrangian structure \begin{document}$ (\omega,\mathcal{F}_{1},\mathcal{F}_{2}) $\end{document}. That is, \begin{document}$ \omega $\end{document} is a symplectic form and \begin{document}$ (\mathcal{F}_{1},\mathcal{F}_{2}) $\end{document} is a pair of transversal Lagrangian foliations
-
Preface to special issue dedicated to tony bloch: Part II Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Leonardo Colombo,Manuel de León,Tomoki Ohsawa
-
Nonlinear dispersion in wave-current interactions Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Darryl D. Holm,Ruiao Hu
Via a sequence of approximations of the Lagrangian in Hamilton's principle for dispersive nonlinear gravity waves we derive a hierarchy of Hamiltonian models for describing wave-current interaction (WCI) in nonlinear dispersive wave dynamics on free surfaces. A subclass of these WCI Hamiltonians admits emergent singular solutions for certain initial conditions. These singular solutions are identified
-
Multi-agent systems for quadcopters Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Richard Carney,Monique Chyba,Chris Gray,George Wilkens,Corey Shanbrom
Unmanned Aerial Vehicles (UAVs) have been increasingly used in the context of remote sensing missions such as target search and tracking, mapping, or surveillance monitoring. In the first part of our paper we consider agent dynamics, network topologies, and collective behaviors. The objective is to enable multiple UAVs to collaborate toward a common goal, as one would find in a remote sensing setting
-
Riemannian cubics close to geodesics at the boundaries Commun. Anal. Mech. (IF 0.8) Pub Date : 2022-01-01 Margarida Camarinha,Fátima Silva Leite,Peter Crouch
In this paper we investigate the existence and uniqueness of Riemannian cubics under boundary conditions on position and velocity. We restrict the study to cubics close to geodesics at the boundaries. In other words, we consider the boundary data in a neighborhood of geodesic boundary data. We define a map that generalizes the Riemannian exponential, the biexponential. This map is used to establish
-
Dimension reduction in recurrent networks by canonicalization Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-11-10 Lyudmila Grigoryeva, Juan-Pablo Ortega
Many recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical state-space realization is adapted in this paper to accommodate semi-infinite inputs so that it can be used as a dimension reduction tool in the recurrent networks setup. The so-called input forgetting property is identified as the key hypothesis that guarantees
-
Poisson double structures Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-12-03 Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these objects are related by differentiation and integration. We use these results to revisit Lie 2-bialgebras by means of Poisson double structures.
-
Quotients of double vector bundles and multigraded bundles Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-10-25 Eckhard Meinrenken
We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower of affine bundles. Applications of the theory include a construction of normal bundles for weighted submanifolds, as well as for pairs of submanifolds with clean intersection.
-
Symplectic $ {\mathbb Z}_2^n $-manifolds Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-19 Andrew James Bruce, Janusz Grabowski
Roughly speaking, $ {\mathbb Z}_2^n $-manifolds are 'manifolds' equipped with $ {\mathbb Z}_2^n $-graded commutative coordinates with the sign rule being determined by the scalar product of their $ {\mathbb Z}_2^n $-degrees. We examine the notion of a symplectic $ {\mathbb Z}_2^n $-manifold, i.e., a $ {\mathbb Z}_2^n $-manifold equipped with a symplectic two-form that may carry non-zero $ {\mathbb
-
Local and global integrability of Lie brackets Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-09-09 Rui L. Fernandes, Yuxuan Zhang
We survey recent results on the local and global integrability of a Lie algebroid, as well as the integrability of infinitesimal multiplicative geometric structures on it.
-
Transitive double Lie algebroids via core diagrams Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-26 Madeleine Jotz Lean, Kirill C. H. Mackenzie
The core diagram of a double Lie algebroid consists of the core of the double Lie algebroid, together with the two core-anchor maps to the sides of the double Lie algebroid. If these two core-anchors are surjective, then the double Lie algebroid and its core diagram are called transitive. This paper establishes an equivalence between transitive double Lie algebroids, and transitive core diagrams over
-
Local convexity for second order differential equations on a Lie algebroid Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-19 Juan Carlos Marrero, David Martín de Diego, Eduardo Martínez
A theory of local convexity for a second order differential equation (${\text{sode}}$) on a Lie algebroid is developed. The particular case when the ${\text{sode}}$ is homogeneous quadratic is extensively discussed.
-
Explicit solutions of the kinetic and potential matching conditions of the energy shaping method Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-24 Sergio Grillo, Leandro Salomone, Marcela Zuccalli
In the context of underactuated Hamiltonian systems defined by simple Hamiltonian functions, the matching conditions of the energy shaping method split into two decoupled subsets of equations: the kinetic and potential equations. The unknown of the kinetic equation is a metric on the configuration space of the system, while the unknown of the potential equation are the same metric and a positive-definite
-
Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-23 Willy Sarlet, Tom Mestdag
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather unusual approach because velocity-dependent transformations in general do not preserve the second-order character of differential equations. Moreover, at least in
-
Error analysis of forced discrete mechanical systems Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-19 Javier Fernández, Sebastián Elías Graiff Zurita, Sergio Grillo
The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Essentially, we prove that when a discretization of contact order $ r $ of the Lagrangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over $ TQ $, where we study the
-
On computational Poisson geometry I: Symbolic foundations Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-19 Miguel Ángel Evangelista-Alvarado, José Crispín Ruíz-Pantaleón, Pablo Suárez-Serrato
We present a computational toolkit for (local) Poisson-Nijenhuis calculus on manifolds. Our Python module $\textsf{PoissonGeometry}$ implements our algorithms and accompanies this paper. Examples of how our methods can be used are explained, including gauge transformations of Poisson bivector in dimension 3, parametric Poisson bivector fields in dimension 4, and Hamiltonian vector fields of parametric
-
Holonomy transformations for Lie subalgebroids Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-08-06 Marco Zambon
Given a foliation, there is a well-known notion of holonomy, which can be understood as an action that differentiates to the Bott connection on the normal bundle. We present an analogous notion for Lie subalgebroids, consisting of an effective action of the minimal integration of the Lie subalgebroid, and provide an explicit description in terms of conjugation by bisections. The construction is done
-
Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-07-23 Jacky Cresson, Fernando Jiménez, Sina Ober-Blöbaum
We prove a Noether's theorem of the first kind for the so-called restricted fractional Euler-Lagrange equations and their discrete counterpart, introduced in [26,27], based in previous results [11,35]. Prior, we compare the restricted fractional calculus of variations to the asymmetric fractional calculus of variations, introduced in [14], and formulate the restricted calculus of variations using the
-
From Schouten to Mackenzie: Notes on brackets Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-07-15 Yvette Kosmann-Schwarzbach
In this paper, dedicated to the memory of Kirill Mackenzie, I relate the origins and early development of the theory of graded Lie brackets, first in the publications on differential geometry of Schouten, Nijenhuis, and Frölicher–Nijenhuis, then in the work of Gerstenhaber and Nijenhuis–Richardson in cohomology theory.
-
Brackets by any other name Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-07-15 Jim Stasheff
Brackets by another name - Whitehead or Samelson products - have a history parallel to that in Kosmann-Schwarzbach's "From Schouten to Mackenzie: notes on brackets". Here I sketch the development of these and some of the other brackets and products and braces within homotopy theory and homological algebra and with applications to mathematical physics. In contrast to the brackets of Schouten, Nijenhuis
-
Matched pair analysis of the Vlasov plasma Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-05-21 Oǧul Esen, Serkan Sütlü
We present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion
-
A bundle framework for observer design on smooth manifolds with symmetry Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-06-28 Anant A. Joshi, D. H. S. Maithripala, Ravi N. Banavar
The article presents a bundle framework for nonlinear observer design on a manifold with a a Lie group action. The group action on the manifold decomposes the manifold to a quotient structure and an orbit space, and the problem of observer design for the entire system gets decomposed to a design over the orbit (the group space) and a design over the quotient space. The emphasis throughout the article
-
Erratum: Constraint algorithm for singular field theories in the \begin{document}$ k $\end{document}-cosymplectic framework Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-05-12 Xavier Gràcia, Xavier Rivas, Narciso Román-Roy
Erratum note for "Constraint algorithm for singular field theories in the $ k $-cosymplectic framework".
-
Retraction: From Schouten to Mackenzie: Notes on brackets Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-06-04
Journal of Geometric Mechanics, (2021) This article was accidentally posted online but only to be discovered that the same article had been published (see [1]) in the same journal. Thus this publication is retracted. The Editorial Office offers apologies for the confusion and inconvenience it might have caused.
-
Schwinger's picture of quantum mechanics: 2-groupoids and symmetries Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-05-12 Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo, Luca Schiavone
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced. It is shown that, given a groupoid $ G\rightrightarrows \Omega $ associated with a (quantum) system, there are two possible descriptions of its symmetries, one "microscopic", the other one "global". The microscopic point of view leads to the introduction
-
On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-05-12 Johannes Huebschmann
This is an overview of ideas related to brackets in early homotopy theory, crossed modules, the obstruction 3-cocycle for the nonabelian extension problem, the Teichmüller cocycle, Lie-Rinehart algebras, Lie algebroids, and differential algebra.
-
On twistor almost complex structures Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-04-25 Michel Cahen, Simone Gutt, John Rawnsley
In this paper we look at the question of integrability, or not, of the two natural almost complex structures $ J^{\pm}_\nabla $ defined on the twistor space $ J(M, g) $ of an even-dimensional manifold $ M $ with additional structures $ g $ and $ \nabla $ a $ g $-connection. We measure their non-integrability by the dimension of the span of the values of $ N^{J^\pm_\nabla} $. We also look at the question
-
Quasi-bi-Hamiltonian structures and superintegrability: Study of a Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-02-02 Manuel F. Rañada
The existence of quasi-bi-Hamiltonian structures for a two-dimen-sional superintegrable $ (k_1,k_2,k_3) $-dependent Kepler-related problem is studied. We make use of an approach that is related with the existence of some complex functions which satisfy interesting Poisson bracket relations and that was previously applied to the standard Kepler problem as well as to some particular superintegrable systems
-
The principle of virtual work and Hamilton's principle on Galilean manifolds Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-01-11 Giuseppe Capobianco, Tom Winandy, Simon R. Eugster
To describe time-dependent finite-dimensional mechanical systems, their generalized space-time is modeled as a Galilean manifold. On this basis, we present a geometric mechanical theory that unifies Lagrangian and Hamiltonian mechanics. Moreover, a general definition of force is given, such that the theory is capable of treating nonpotential forces acting on a mechanical system. Within this theory
-
Erratum for "Error analysis of forced discrete mechanical systems" Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-01-01 Javier Fernández,Sebastián Elías Graiff Zurita,Sergio Grillo
-
Book review: General theory of Lie groupoids and Lie algebroids, by Kirill C. H. Mackenzie Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-01-01 Theodore Voronov
-
Preface to special issue in honor of Kirill C. H. Mackenzie Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-01-01 Iakovos Androulidakis,Henrique Bursztyn,Juan-Carlos Marrero,Alan Weinstein
-
Preface to the special issue dedicated to anthony bloch Commun. Anal. Mech. (IF 0.8) Pub Date : 2021-01-01 Leonardo Colombo,Manuel de León,Tomoki Ohsawa
JOURNAL OF GEOMETRIC MECHANICS doi:10 3934/jgm 2021004 ©American Institute of Mathematical Sciences Volume 13, Number 1, March 2021 pp i{iii PREFACE TO THE SPECIAL ISSUE DEDICATED TO ANTHONY BLOCH This volume of JGM is dedicated to Tony Bloch on the occasion of his 65th birthday Perhaps PREFACE TO THE SPECIAL ISSUE DEDICATED TO ANTHONY BLOCH iii this was the time he managed to spare for his research
-
Contact Hamiltonian and Lagrangian systems with nonholonomic constraints Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-12-28 Manuel de León, Víctor M. Jiménez, Manuel Lainz
In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which
-
Lagrangian reduction of nonholonomic discrete mechanical systems by stages Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-11-06 Javier Fernández, Cora Tori, Marcela Zuccalli
In this work we introduce a category $ \mathfrak{L D P}_{d} $ of discrete-time dynamical systems, that we call discrete Lagrange–D'Alembert–Poincaré systems, and study some of its elementary properties. Examples of objects of $ \mathfrak{L D P}_{d} $ are nonholonomic discrete mechanical systems as well as their lagrangian reductions and, also, discrete Lagrange-Poincaré systems. We also introduce a
-
Symmetry actuated closed-loop Hamiltonian systems Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-11-06 Simon Hochgerner
This paper extends the theory of controlled Hamiltonian systems with symmetries due to [23,9,10,6,7,11] to the case of non-abelian symmetry groups $ G $ and semi-direct product configuration spaces. The notion of symmetry actuating forces is introduced and it is shown, that Hamiltonian systems subject to such forces permit a conservation law, which arises as a controlled perturbation of the $ G $-momentum
-
Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-11-23 Bernard Bonnard, Jérémy Rouot
A recent force-fatigue parameterized mathematical model, based on the seminal contributions of V. Hill to describe muscular activity, allows to predict the muscular force response to external electrical stimulation (FES) and it opens the road to optimize the FES-input to maximize the force response to a pulse train, to track a reference force while minimizing the fatigue for a sequence of pulse trains
-
A Lagrangian approach to extremal curves on Stiefel manifolds Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-11-06 Knut Hüper, Irina Markina, Fátima Silva Leite
A unified framework for studying extremal curves on real Stiefel manifolds is presented. We start with a smooth one-parameter family of pseudo-Riemannian metrics on a product of orthogonal groups acting transitively on Stiefel manifolds. In the next step Euler-Langrange equations for a whole class of extremal curves on Stiefel manifolds are derived. This includes not only geodesics with respect to
-
Control of locomotion systems and dynamics in relative periodic orbits Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-07-28 Francesco Fassò, Simone Passarella, Marta Zoppello
The connection between the dynamics in relative periodic orbits of vector fields with noncompact symmetry groups and periodic control for the class of control systems on Lie groups known as '(robotic) locomotion systems' is well known, and has led to the identification of (geometric) phases. We take an approach which is complementary to the existing ones, advocating the relevance——for trajectory generation
-
Higher order normal modes Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-09-01 Giuseppe Gaeta, Sebastian Walcher
Normal modes are intimately related to the quadratic approximation of a potential at its hyperbolic equilibria. Here we extend the notion to the case where the Taylor expansion for the potential at a critical point starts with higher order terms, and show that such an extension shares some of the properties of standard normal modes. Some symmetric examples are considered in detail.
-
Some remarks about the centre of mass of two particles in spaces of constant curvature Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-07-28 Luis C. García-Naranjo
The concept of centre of mass of two particles in 2D spaces of constant Gaussian curvature is discussed by recalling the notion of "relativistic rule of lever" introduced by Galperin [6] (Comm. Math. Phys. 154 (1993), 63–84), and comparing it with two other definitions of centre of mass that arise naturally on the treatment of the 2-body problem in spaces of constant curvature: firstly as the collision
-
Characterization of toric systems via transport costs Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-09-07 Sonja Hohloch
We characterize completely integrable Hamiltonian systems inducing an effective Hamiltonian torus action as systems with zero transport costs w.r.t. the time-$ T $ map where $ T\in \mathbb{R}^n $ is the period of the acting $ n $-torus.
-
Angular momentum coupling, Dirac oscillators, and quantum band rearrangements in the presence of momentum reversal symmetries Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-07-28 Toshihiro Iwai, Dmitrií A. Sadovskií, Boris I. Zhilinskií
We investigate the elementary rearrangements of energy bands in slow-fast one-parameter families of systems whose fast subsystem possesses a half-integer spin. Beginning with a simple case without any time-reversal symmetries, we analyze and compare increasingly sophisticated model Hamiltonians with these symmetries. The models are inspired by the time-reversal modification of the Berry phase setup
-
Getting into the vortex: On the contributions of james montaldi Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-08-09 Jair Koiller
James Montaldi's expertises span many areas on pure and applied mathematics. I will discuss here just one, his contributions to the motion of point vortices, specially the role of symmetries in the bifurcations and stability of equilibrium configurations in surfaces of constant curvature. This approach leads, for instance, to a very elegant proof of a classical result, the nonlinear stability of Thompson's
-
Continuous singularities in hamiltonian relative equilibria with abelian momentum isotropy Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-07-28 Miguel Rodríguez-Olmos
We survey several aspects of the qualitative dynamics around Hamiltonian relative equilibria. We pay special attention to the role of continuous singularities and its effect in their stability, persistence and bifurcations. Our approach is semi-global using extensively the Hamiltonian tube of Marle, Guillemin and Sternberg.
-
Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-09-01 Sergey Rashkovskiy
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the configuration space and described by the continual equation of motion and the continuity equation. For Hamiltonian systems, the usual Hamilton-Jacobi equations naturally
-
Linearization of the higher analogue of Courant algebroids Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-09-01 Honglei Lang, Yunhe Sheng
In this paper, we show that the spaces of sections of the $ n $-th differential operator bundle $ \mathfrak{D}^n E $ and the $ n $-th skew-symmetric jet bundle $ \mathfrak{J}_n E $ of a vector bundle $ E $ are isomorphic to the spaces of linear $ n $-vector fields and linear $ n $-forms on $ E^* $ respectively. Consequently, the $ n $-omni-Lie algebroid $ \mathfrak{D} E\oplus \mathfrak{J}_n E $ introduced
-
On nomalized differentials on spectral curves associated with the sinh-gordon equation Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-07-28 Thomas Kappeler, Yannick Widmer
The spectral curve associated with the sinh-Gordon equation on the torus is defined in terms of the spectrum of the Lax operator appearing in the Lax pair formulation of the equation. If the spectrum is simple, it is an open Riemann surface of infinite genus. In this paper we construct normalized differentials on this curve and derive estimates for the location of their zeroes, needed for the construction
-
A family of multiply warped product semi-riemannian einstein metrics Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-07-28 Buddhadev Pal, Pankaj Kumar
In this paper, we characterize multiply warped product semi -Riemannian manifolds when the base is conformal to an $ n $-dimensional pseudo-Euclidean space. We prove some conditions on warped product semi- Riemannian manifolds to be an Einstein manifold which is invariant under the action of an $ (n-1) $-dimensional translation group. After that we apply this result for the case of Ricci-flat multiply
-
Nonholonomic and constrained variational mechanics Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-06-02 Andrew D. Lewis
Equations governing mechanical systems with nonholonomic constraints can be developed in two ways: (1) using the physical principles of Newtonian mechanics; (2) using a constrained variational principle. Generally, the two sets of resulting equations are not equivalent. While mechanics arises from the first of these methods, sub-Riemannian geometry is a special case of the second. Thus both sets of
-
A note on Hybrid Routh reduction for time-dependent Lagrangian systems Commun. Anal. Mech. (IF 0.8) Pub Date : 2020-06-02 Leonardo J. Colombo, María Emma Eyrea Irazú, Eduardo García-Toraño Andrés
This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results for continuous-time systems. We illustrate the applicability of the method using the example of a billiard with moving walls.