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Journal of Geometric Mechanics最新文献

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Parametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit 椭圆轨道上变长质心双摆的参数稳定性
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2021031
José Laudelino de Menezes Neto, G. C. Araujo, Yocelyn Pérez Rothen, C. Vidal
{"title":"Parametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit","authors":"José Laudelino de Menezes Neto, G. C. Araujo, Yocelyn Pérez Rothen, C. Vidal","doi":"10.3934/jgm.2021031","DOIUrl":"https://doi.org/10.3934/jgm.2021031","url":null,"abstract":"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 space of the parameters associated with the pendulum length and the eccentricity of the orbit.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78874108","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 dedicated to Tony Bloch: Part Ⅲ 托尼-布洛赫特刊序言：第Ⅲ部分
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022020
Leonardo Colombo, M. de León, T. Ohsawa
{"title":"Preface to special issue dedicated to Tony Bloch: Part Ⅲ","authors":"Leonardo Colombo, M. de León, T. Ohsawa","doi":"10.3934/jgm.2022020","DOIUrl":"https://doi.org/10.3934/jgm.2022020","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"57 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85419890","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
Atmospheric Ekman flows with uniform density in ellipsoidal coordinates: Explicit solution and dynamical properties 椭球坐标下均匀密度的大气Ekman流:显式解和动力学性质
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022015
Taoyu Yang, Michal Feckan, Jinrong Wang
{"title":"Atmospheric Ekman flows with uniform density in ellipsoidal coordinates: Explicit solution and dynamical properties","authors":"Taoyu Yang, Michal Feckan, Jinrong Wang","doi":"10.3934/jgm.2022015","DOIUrl":"https://doi.org/10.3934/jgm.2022015","url":null,"abstract":"In this paper, we present a new general system of equations describing the steady motion of atmosphere with uniform density in ellipsoidal coordinates, which is derived from the general governing equations for viscous fluids. We first show that this new system can be reduced to the classic Ekman equations. Secondly, we obtain the explicit solution of the Ekman equations in ellipsoidal coordinates. Thirdly, for the viscosity related to the height, we obtain the solution of the classical problem with zero acceleration at the bottom of Ekman layer. Finally, the uniqueness and dynamical properties of solution are demonstrated.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"35 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82110705","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
Riemannian cubics close to geodesics at the boundaries 边界处接近测地线的黎曼立方
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022003
M. Camarinha, F. Silva Leite, P. Crouch
{"title":"Riemannian cubics close to geodesics at the boundaries","authors":"M. Camarinha, F. Silva Leite, P. Crouch","doi":"10.3934/jgm.2022003","DOIUrl":"https://doi.org/10.3934/jgm.2022003","url":null,"abstract":"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 the correspondence between initial and boundary data. We also emphasize the relation between biconjugate points and bi-Jacobi fields along cubics by means of the biexponential map.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"14 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89980215","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: 4
Kirill Mackenzie, Bangor and holonomy 基里尔-麦肯齐（Kirill Mackenzie），班戈和整体论
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022012
Ronald Brown
{"title":"Kirill Mackenzie, Bangor and holonomy","authors":"Ronald Brown","doi":"10.3934/jgm.2022012","DOIUrl":"https://doi.org/10.3934/jgm.2022012","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"1974 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90222067","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
Preface to special issue dedicated to tony bloch: Part II 托尼-布洛赫特刊序言：第二部分
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022005
Leonardo Colombo, M. de León, T. Ohsawa
{"title":"Preface to special issue dedicated to tony bloch: Part II","authors":"Leonardo Colombo, M. de León, T. Ohsawa","doi":"10.3934/jgm.2022005","DOIUrl":"https://doi.org/10.3934/jgm.2022005","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78514212","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
Modeling student engagement using optimal control theory 利用最优控制理论建模学生参与
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2021032
D. Lewis
{"title":"Modeling student engagement using optimal control theory","authors":"D. Lewis","doi":"10.3934/jgm.2021032","DOIUrl":"https://doi.org/10.3934/jgm.2021032","url":null,"abstract":"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 resources for other activities, and psychological stresses related to engagement with the learning task. Application of Pontryagin's maximum principle to some simple models of engagement yields solutions of the synthesis problem mimicking familiar behaviors including avoidance, procrastination, and increasing commitment in response to increasing mastery.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"91 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81563723","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
Preface to special issue in honor of Kirill C. H. Mackenzie: Part Ⅱ 纪念 Kirill C. H. Mackenzie 特刊序言：第二部分
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022016
Iakovos Androulidakis, Henrique Burzstyn, J. Marrero, A. Weinstein
{"title":"Preface to special issue in honor of Kirill C. H. Mackenzie: Part Ⅱ","authors":"Iakovos Androulidakis, Henrique Burzstyn, J. Marrero, A. Weinstein","doi":"10.3934/jgm.2022016","DOIUrl":"https://doi.org/10.3934/jgm.2022016","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"53 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88976928","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
Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles 李群及其切束上全约束和欠约束刚体运动的控制与维持
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022002
Brennan McCann, Morad Nazari
{"title":"Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles","authors":"Brennan McCann, Morad Nazari","doi":"10.3934/jgm.2022002","DOIUrl":"https://doi.org/10.3934/jgm.2022002","url":null,"abstract":"<p style='text-indent:20px;'>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 <inline-formula><tex-math id=\"M1\">begin{document}$ {mathsf{SE}(3)}$end{document}</tex-math></inline-formula> and its second order tangent bundle <inline-formula><tex-math id=\"M2\">begin{document}${mathsf{T}^2mathsf{SE}(3)} $end{document}</tex-math></inline-formula>, is proposed in addition to the formulation development on Euclidean spaces. Then, a Morse-Lyapunov based tracking controller using backstepping is applied to capture disturbed initial conditions that the U-K formulation cannot account for. This theoretical development is then applied to fully-constrained and underconstrained scenarios of rigid-body spacecraft motion in a lunar orbit, and the translational and rotational motions of the spacecraft and the control inputs obtained using the proposed methodologies to achieve and maintain those constrained motions are studied.</p>","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"52 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73664642","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
On embedding of subcartesian differential space and application 次笛卡儿微分空间的嵌入及其应用
IF 0.8 4区 数学
Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022007
Qianqian Xia
{"title":"On embedding of subcartesian differential space and application","authors":"Qianqian Xia","doi":"10.3934/jgm.2022007","DOIUrl":"https://doi.org/10.3934/jgm.2022007","url":null,"abstract":"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 and smooth generalized subbundles of vector bundles on subcartesian spaces are globally finitely generated. We show that every algebra isomorphism between the associative algebras of all smooth functions on two subcartesian differential spaces is the pullback by a smooth diffeomorphism between these two spaces.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":"45 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77574704","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
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