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The angular motion of oceanic vortex formations 海洋涡旋形成的角运动
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-06-14 DOI: 10.1016/j.jappmathmech.2018.03.007
E.K. Lavrovskii, V.V. Fominykh
{"title":"The angular motion of oceanic vortex formations","authors":"E.K. Lavrovskii,&nbsp;V.V. Fominykh","doi":"10.1016/j.jappmathmech.2018.03.007","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.007","url":null,"abstract":"<div><p><span>Within the framework of the rigid body hypothesis, the influence of external torques acting on a rotating water lens in a stratified ocean is examined and a hypothesis about the angular motion of objects of such kind is constructed. The structure of the external torques acting on the lens is investigated and their magnitudes and influence on the overall picture of the motion of the lens about its centre of mass are estimated. It is shown that the hydrostatic buoyancy torque is the most important of such torques, it being orders of magnitude greater than the Coriolis torque and the torque due to virtual masses, and also the gravitational torque and other torques. The </span>friction torque can promote stabilization of the angular motion and lead to the appearance of a steady regime. The results obtained are in agreement with the observed motion of oceanic formations.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 390-394"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91724953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Limit periodic motions in systems with after-effect in a critical case* 临界情况下具有后效应系统的周期运动极限*
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-06-14 DOI: 10.1016/j.jappmathmech.2018.03.001
V.S. Sergeev
{"title":"Limit periodic motions in systems with after-effect in a critical case*","authors":"V.S. Sergeev","doi":"10.1016/j.jappmathmech.2018.03.001","DOIUrl":"10.1016/j.jappmathmech.2018.03.001","url":null,"abstract":"<div><p>Systems with after-effect are considered, whose states are described by Volterra integro-differential equations. The critical case of one zero root of the characteristic equation is investigated (where all the other roots have negative real parts) along with the question of the existence in this case of limit periodic motions of the system, i.e., motions which tend exponentially to periodic regimes with unbounded increase of time. A time-dependent, small, piecewise-continuous limit periodic perturbation, generated by external factors, is present in the system. It is shown that in the system under the perturbation, limit periodic motions arise that are represented by power series in fractional powers of a small parameter characterizing the perturbation magnitude. As an example, rotational limit periodic oscillations of a solid plate in an air flow are considered with time dependence of the flow about the plate taken into account by introducing integral terms into the aerodynamic torque.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 343-350"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72545525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix method of constructing the differential equations of motion of an exoskeleton and its control 构造外骨骼运动微分方程及其控制的矩阵法
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-05-07 DOI: 10.1016/j.jappmathmech.2018.03.002
A.V. Borisov , G.M. Rozenblat
{"title":"Matrix method of constructing the differential equations of motion of an exoskeleton and its control","authors":"A.V. Borisov ,&nbsp;G.M. Rozenblat","doi":"10.1016/j.jappmathmech.2018.03.002","DOIUrl":"10.1016/j.jappmathmech.2018.03.002","url":null,"abstract":"<div><p><span>Two mathematical models of rods of variable length from which an exoskeleton can be created, providing comfortable movement of a human in it owing to duplication of the properties of a motion-support apparatus, are considered. Their structure is elucidated on the basis of an analysis of the differential equations of motion, allowing for representing them in vector-matrix form. General regularities of the construction of the matrix elements entering into the </span>system of differential equations of motion are established and generalizing formulae for the matrix elements are obtained. A new matrix method of constructing the differential equations of motion is presented and illustrated by a specific example. This system of equations is solved numerically. The possibility of reinforcing the control actions for control of the exoskeleton motion with a human inside it is considered.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 351-359"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87247554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
The approach problem of a nonlinear controlled system in a finite time interval 有限时间区间内非线性控制系统的逼近问题
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-10-07 DOI: 10.1016/j.jappmathmech.2017.08.005
A.R. Matviychuk, V.I. Ukhobotov, A.V. Ushakov, V.N. Ushakov
{"title":"The approach problem of a nonlinear controlled system in a finite time interval","authors":"A.R. Matviychuk,&nbsp;V.I. Ukhobotov,&nbsp;A.V. Ushakov,&nbsp;V.N. Ushakov","doi":"10.1016/j.jappmathmech.2017.08.005","DOIUrl":"10.1016/j.jappmathmech.2017.08.005","url":null,"abstract":"<div><p>A nonlinear controlled system in Euclidean space, which is specified in a finite time interval, is considered. The approach problem of a controlled system with a target set in a finite time interval is studied. An algorithm for an approximate calculation of the solution of the problem is presented. An illustrative example of a “flywheel–pendulum” controlled mechanical system is considered.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 2","pages":"Pages 114-128"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.08.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76867444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Method for the analysis of long water waves taking into account reflection from a gently sloping beach 考虑缓倾斜海滩反射的长水波分析方法
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-08-17 DOI: 10.1016/j.jappmathmech.2017.07.003
D.A. Lozhnikov, V.E. Nazaikinskii
{"title":"Method for the analysis of long water waves taking into account reflection from a gently sloping beach","authors":"D.A. Lozhnikov,&nbsp;V.E. Nazaikinskii","doi":"10.1016/j.jappmathmech.2017.07.003","DOIUrl":"10.1016/j.jappmathmech.2017.07.003","url":null,"abstract":"<div><p>Algorithms and their software implementation are described that allow calculating the front propagation for a long wave (for example, a tsunami wave) described in the approximation of the linearized shallow water equations with reflection from a shallow beach taken into account. The algorithms are based on a construction of asymptotic solutions<span> of the Cauchy problem for hyperbolic equations with degeneracy on the boundary earlier proposed with the participation of one of the authors. The results of a numerical experiment are presented.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 21-28"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84323971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Modelling of the elastoplastic dynamics of longitudinally reinforced wall beams based on a time-explicit central difference method 基于时间显式中心差分法的纵向加固墙梁弹塑性动力学建模
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-08-26 DOI: 10.1016/j.jappmathmech.2017.07.005
A.P. Yankovskii
{"title":"Modelling of the elastoplastic dynamics of longitudinally reinforced wall beams based on a time-explicit central difference method","authors":"A.P. Yankovskii","doi":"10.1016/j.jappmathmech.2017.07.005","DOIUrl":"10.1016/j.jappmathmech.2017.07.005","url":null,"abstract":"<div><p><span><span>A numerical analytical method for modelling the elastoplastic deformation of longitudinally reinforced wall beams with isotropically strengthened composite component materials, which enables a solution of the corresponding elastoplastic problem to be obtained at discrete instants of time using an explicit scheme, is developed by a time step method involving central finite differences. In the case of linear elastic composite component materials in the reinforced beams, the proposed model reduces to Bolotin's well-known structural model of the mechanics of composites. An initial-boundary-value problem of the dynamic deformation of longitudinally reinforced flexible wall beams is formulated in the von Karman approximation with consideration of their weakened resistance to transverse </span>shearing. Equations and relations corresponding to two versions of Timoshenko's theory are obtained from a few positions. An explicit “cross” scheme for numerical integration of the initial-boundary-value problem posed, which is consistent with the step-by-step scheme used to model the elastoplastic deformation of a composite beam material, is constructed. Calculations of the dynamic and quasistatic </span>bending behaviour of reinforced wall beams during the linear elastic and elastoplastic deformation of the composite component materials are performed. It is found that the classical theory is totally unacceptable for performing such calculations (except for beams of very small relative height) and that the first version of Timoshenko's theory gives adequate results only in the case of linear elastic composite component materials. Use of the second version of Timoshenko's theory is recommended as more accurate for calculations of the elastoplastic deformation of reinforced wall beams.</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 36-51"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89170312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
The stability of the motion of a non-axisymmetric body in a resistive medium 非轴对称物体在电阻介质中运动的稳定性
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-05-07 DOI: 10.1016/j.jappmathmech.2018.03.014
K. Yu. Osipenko
{"title":"The stability of the motion of a non-axisymmetric body in a resistive medium","authors":"K. Yu. Osipenko","doi":"10.1016/j.jappmathmech.2018.03.014","DOIUrl":"10.1016/j.jappmathmech.2018.03.014","url":null,"abstract":"<div><p><span>A mathematical model of the plane motion of a non-axisymmetric body in a resistive medium is constructed using the local interaction method. Criteria for the stability of </span>rectilinear<span> motion are obtained in a general form in the case of a frozen axial velocity<span>. The stability of the motion of a regular triangular pyramid is investigated in detail when a constant friction and pressure, specified using an empirical Poncelet formula in the form of a sum of inertial and strength terms, acts on its lateral surface. The stabilities of a pyramid and a cone are compared. The effect of deceleration on the stability of the rectilinear motion is considered.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 455-462"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72410025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Cavitation flow of an ideal incompressible fluid in the electrochemical machining of metals 金属电解加工中理想不可压缩流体的空化流
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2017-08-14 DOI: 10.1016/j.jappmathmech.2017.07.004
N.M. Minazetdinov
{"title":"Cavitation flow of an ideal incompressible fluid in the electrochemical machining of metals","authors":"N.M. Minazetdinov","doi":"10.1016/j.jappmathmech.2017.07.004","DOIUrl":"10.1016/j.jappmathmech.2017.07.004","url":null,"abstract":"<div><p>The limiting simplest model of the non-linear two-dimensional problem of the electrochemical machining of metals taking account of the attached cavitation<span> is constructed on the basis of a model of an ideal electrochemical shaping process and the theory of ideal incompressible fluid jets. A solution is obtained related to the determination of the steady shape of the surface of the component (anode) taking account of the cavity formed in the machining on the cathode tool boundary. The results of the calculations show that the model reflects the qualitative effects related to the effect of the added cavity on the shape of the machined component.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 29-35"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77540817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Steady rotations of a satellite with internal elastic and dissipative forces 具有内部弹性和耗散力的卫星的稳定旋转
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/J.JAPPMATHMECH.2018.03.011
N. Amelkin, V. Kholoshchak
{"title":"Steady rotations of a satellite with internal elastic and dissipative forces","authors":"N. Amelkin, V. Kholoshchak","doi":"10.1016/J.JAPPMATHMECH.2018.03.011","DOIUrl":"https://doi.org/10.1016/J.JAPPMATHMECH.2018.03.011","url":null,"abstract":"","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"13 1","pages":"431-441"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74297668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Internal gravity waves excited by a pulsating perturbation source 由脉动扰动源激发的内部重力波
Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 Epub Date: 2018-05-07 DOI: 10.1016/j.jappmathmech.2018.03.006
V.V. Bulatov, Yu.V. Vladimirov
{"title":"Internal gravity waves excited by a pulsating perturbation source","authors":"V.V. Bulatov,&nbsp;Yu.V. Vladimirov","doi":"10.1016/j.jappmathmech.2018.03.006","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.006","url":null,"abstract":"<div><p><span>The problem of an internal gravity wave field from a pulsating point source of perturbations in the flow of a stratified medium of finite depth with horizontal velocity of the source </span><em>V</em><span> less than the maximum value of the group velocity of the internal gravity waves </span><em>c</em> is considered, unlike to the previously considered case <em>V</em> <!-->&gt;<!--> <em>c</em><span>. Constructed asymptotic solutions make it possible to describe the amplitude-phase characteristics of individual modes comprising the full field of internal gravity waves. The excited waves consist of waves of two types: ring-like waves and wedge-shaped waves. Features of the mode structure of the excited fields are considered as functions of the parameters of the stratified medium and the characteristics of the perturbation source.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 384-389"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91724952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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