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Journal of Geometric Mechanics最新文献

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A unifying approach for rolling symmetric spaces 滚动对称空间的统一方法
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI: 10.3934/jgm.2020016
K. Krakowski, L. Machado, F. Leite
{"title":"A unifying approach for rolling symmetric spaces","authors":"K. Krakowski, L. Machado, F. Leite","doi":"10.3934/jgm.2020016","DOIUrl":"https://doi.org/10.3934/jgm.2020016","url":null,"abstract":"The main goal of this paper is to present a unifying theory to describe the pure rolling motions of Riemannian symmetric spaces, which are submanifolds of Euclidean or pseudo-Euclidean spaces. Rolling motions provide interesting examples of nonholonomic systems and symmetric spaces appear associated to important applications. We make a connection between the structure of the kinematic equations of rolling and the natural decomposition of the Lie algebra associated to the symmetric space. This emphasises the relevance of Lie theory in the geometry of rolling manifolds and explains why many particular examples scattered through the existing literature always show a common pattern.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89848172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model 利用非等距力-疲劳模型控制功能性电刺激下肌肉力响应的几何优化技术
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI: 10.3934/jgm.2020032
B. Bonnard, J. Rouot
{"title":"Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model","authors":"B. Bonnard, J. Rouot","doi":"10.3934/jgm.2020032","DOIUrl":"https://doi.org/10.3934/jgm.2020032","url":null,"abstract":"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 or to follow a reference joint angle trajectory to produce motion in the non-isometric case. In this article, we introduce the geometric frame to analyze the dynamics and we present Pontryagin types necessary optimality conditions adapted to digital controls, used in the experiments, vs permanent control and which fits in the optimal sampled-data control frame. This leads to Hamiltonian differential variational inequalities, which can be numerically implemented vs direct optimization schemes.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"68 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91237346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Erratum for "Error analysis of forced discrete mechanical systems" "强制离散机械系统的误差分析 "勘误表
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI: 10.3934/jgm.2021030
J. Fernández, S. G. Zurita, S. Grillo
{"title":"Erratum for \"Error analysis of forced discrete mechanical systems\"","authors":"J. Fernández, S. G. Zurita, S. Grillo","doi":"10.3934/jgm.2021030","DOIUrl":"https://doi.org/10.3934/jgm.2021030","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79030061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations 有限变分法中的连续和离散Noether分数守恒量
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI: 10.3934/jgm.2021012
J. Cresson, F. Jiménez, S. Ober-Blöbaum
{"title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","authors":"J. Cresson, F. Jiménez, S. Ober-Blöbaum","doi":"10.3934/jgm.2021012","DOIUrl":"https://doi.org/10.3934/jgm.2021012","url":null,"abstract":"<p style='text-indent:20px;'>We prove a Noether's theorem of the first kind for the so-called <i>restricted fractional Euler-Lagrange equations</i> and their discrete counterpart, introduced in [<xref ref-type=\"bibr\" rid=\"b26\">26</xref>,<xref ref-type=\"bibr\" rid=\"b27\">27</xref>], based in previous results [<xref ref-type=\"bibr\" rid=\"b11\">11</xref>,<xref ref-type=\"bibr\" rid=\"b35\">35</xref>]. Prior, we compare the restricted fractional calculus of variations to the <i>asymmetric fractional calculus of variations</i>, introduced in [<xref ref-type=\"bibr\" rid=\"b14\">14</xref>], and formulate the restricted calculus of variations using the <i>discrete embedding</i> approach [<xref ref-type=\"bibr\" rid=\"b12\">12</xref>,<xref ref-type=\"bibr\" rid=\"b18\">18</xref>]. The two theories are designed to provide a variational formulation of dissipative systems, and are based on modeling irreversbility by means of fractional derivatives. We explicit the role of time-reversed solutions and causality in the restricted fractional calculus of variations and we propose an alternative formulation. Finally, we implement our results for a particular example and provide simulations, actually showing the constant behaviour in time of the discrete conserved quantities outcoming the Noether's theorems.</p>","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73899968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Preface to special issue in honor of Kirill C. H. Mackenzie 纪念基里尔-麦肯齐特刊序言
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI: 10.3934/jgm.2021025
Iakovos Androulidakis, H. Bursztyn, J. Marrero, A. Weinstein
{"title":"Preface to special issue in honor of Kirill C. H. Mackenzie","authors":"Iakovos Androulidakis, H. Bursztyn, J. Marrero, A. Weinstein","doi":"10.3934/jgm.2021025","DOIUrl":"https://doi.org/10.3934/jgm.2021025","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"75 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73741746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Contact Hamiltonian and Lagrangian systems with nonholonomic constraints 具有非完整约束的接触哈密顿系统和拉格朗日系统
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI: 10.3934/jgm.2021001
M. León, V. M. Jiménez, M. Lainz
{"title":"Contact Hamiltonian and Lagrangian systems with nonholonomic constraints","authors":"M. León, V. M. Jiménez, M. Lainz","doi":"10.3934/jgm.2021001","DOIUrl":"https://doi.org/10.3934/jgm.2021001","url":null,"abstract":"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 is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88617135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
Multi-agent systems for quadcopters 四轴飞行器的多智能体系统
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-12-31 DOI: 10.3934/jgm.2021005
Richard Carney, M. Chyba, Chris Gray, Corey Shanbrom, G. Wilkens
{"title":"Multi-agent systems for quadcopters","authors":"Richard Carney, M. Chyba, Chris Gray, Corey Shanbrom, G. Wilkens","doi":"10.3934/jgm.2021005","DOIUrl":"https://doi.org/10.3934/jgm.2021005","url":null,"abstract":"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. An agreement protocol is carried out by the multi-agents using local information, and without external user input. The second part of the paper focuses on the equations of motion for a specific type of UAV, the quadcopter, and expresses them as an affine nonlinear control system. Finally, we illustrate our work with a simulation of an agreement protocol for dynamically sound quadcopters augmenting the particle graph theoretic approach with orientation and a proper dynamics for quadcopters.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78242545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constrained systems, generalized Hamilton-Jacobi actions, and quantization 约束系统，广义Hamilton-Jacobi作用，和量化
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-12-24 DOI: 10.3934/jgm.2022010
A. Cattaneo, P. Mnev, K. Wernli
{"title":"Constrained systems, generalized Hamilton-Jacobi actions, and quantization","authors":"A. Cattaneo, P. Mnev, K. Wernli","doi":"10.3934/jgm.2022010","DOIUrl":"https://doi.org/10.3934/jgm.2022010","url":null,"abstract":"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 (including nonabelian Chern–Simons theory, where the HJ action turns out to be the gauged Wess–Zumino–Witten action). Perturbative quantization, limited in this note to finite-dimensional targets, is performed in the framework of the Batalin–Vilkovisky (BV) formalism in the bulk and of the Batalin–Fradkin–Vilkovisky (BFV) formalism at the endpoints. As a sanity check of the method, it is proved that the semiclassical contribution of the physical part of the evolution operator is still given by the HJ action. Several examples are computed explicitly. In particular, it is shown that the toy model for nonabelian Chern–Simons theory and the toy model for 7D Chern–Simons theory with nonlinear Hitchin polarization do not have quantum corrections in the physical part (the extension of these results to the actual cases is discussed in the companion paper [21]). Background material for both the classical part (symplectic geometry, generalized generating functions, HJ actions, and the extension of these concepts to infinite-dimensional manifolds) and the quantum part (BV-BFV formalism) is provided.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89817874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On twistor almost complex structures 关于扭曲或几乎复杂的结构
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-10-09 DOI: 10.3934/JGM.2021006
M. Cahen, S. Gutt, J. Rawnsley
{"title":"On twistor almost complex structures","authors":"M. Cahen, S. Gutt, J. Rawnsley","doi":"10.3934/JGM.2021006","DOIUrl":"https://doi.org/10.3934/JGM.2021006","url":null,"abstract":"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 also look at the question of the compatibility of $J^{pm}_nabla$ with a natural closed $2$-form $omega^{J(M,g,nabla)}$ defined on $J(M,g)$. For $(M,g)$ we consider either a pseudo-Riemannian manifold, orientable or not, with the Levi Civita connection or a symplectic manifold with a given symplectic connection $nabla$. In all cases $J(M,g)$ is a bundle of complex structures on the tangent spaces of $M$ compatible with $g$ and we denote by $pi colon J(M,g) longrightarrow M$ the bundle projection. In the case $M$ is oriented we require the orientation of the complex structures to be the given one. In the symplectic case the complex structures are positive.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84038069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Some remarks about the centre of mass of two particles in spaces of constant curvature 关于常曲率空间中两个粒子质心的一些注释
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2020-09-28 DOI: 10.3934/jgm.2020020
Luis C. Garc'ia-Naranjo
{"title":"Some remarks about the centre of mass of two particles in spaces of constant curvature","authors":"Luis C. Garc'ia-Naranjo","doi":"10.3934/jgm.2020020","DOIUrl":"https://doi.org/10.3934/jgm.2020020","url":null,"abstract":"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 [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 point of particles that are initially at rest, and secondly as the centre of rotation of steady rotation solutions. It is shown that if the particles have distinct masses then these definitions are equivalent only if the curvature vanishes and instead lead to three different notions of centre of mass in the general case.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"92 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74538885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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