scholarly journals Dynamics of constrained many body problems in constant curvature two-dimensional manifolds

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170425 ◽  
Author(s):  
Andrzej J. Maciejewski ◽  
Maria Przybylska
Keyword(s):  
Constant Curvature ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Rigid Bodies ◽  
The Body ◽  
Two Dimensional ◽  
Many Body ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In this paper, we investigate systems of several point masses moving in constant curvature two-dimensional manifolds and subjected to certain holonomic constraints. We show that in certain cases these systems can be considered as rigid bodies in Euclidean and pseudo-Euclidean three-dimensional spaces with points which can move along a curve fixed in the body. We derive the equations of motion which are Hamiltonian with respect to a certain degenerated Poisson bracket. Moreover, we have found several integrable cases of described models. For one of them, we give the necessary and sufficient conditions for the integrability. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

scholarly journals Experiments on the motion of solid bodies in rotating fluids

1923 ◽  
Vol 104 (725) ◽  
pp. 213-218 ◽  
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Steady Motion ◽  
The Body ◽  
Two Dimensional ◽  
Experimental Conditions ◽  
Axis Of Rotation ◽  
Rotating Liquid ◽  
Steady Motions ◽  
Solid Bodies

Some years ago it was pointed out by Prof. Proudman that all slow steady motions of a rotating liquid must be two-dimensional. If the motion is produced by moving a cylindrical object slowly through the liquid in such a way that its axis remains parallel to the axis of rotation, or if a two-dimensional motion is conceived as already existing, it seems clear that it will remain two-dimensional. If a slow three-dimensional motion is produced, then it cannot be a steady one. On the other hand, if an attempt is made to produce a slow steady motion by moving a three-dimensional body with a small uniform velocity (relative to axes which rotate with the fluid) three possibilities present themselves:— ( a ) The motion in the liquid may never become steady, however long the body goes on moving. ( b ) The motion may be steady but it may not be small in the neighbourhood of the body. ( c ) The motion may be steady and two-dimensional. In considering these three possibilities it seems very unlikely that ( a ) will be the true one. In an infinite rotating fluid the disturbance produced by starting the motion of the body might go on spreading out for ever and steady motion might never be attained, but if the body were moved steadily in a direction at right angles to the axis of rotation, and if the fluid were contained between parallel planes also perpendicular to the axis of rotation, it seems very improbable that no steady motion satisfying the equations of motion could be attained. There is more chance that ( b ) may be true. A class of mathematical expressions representing the steady motion of a sphere along the axis of a rotating liquid has been obtained. This solution of the problem breaks down when the velocity of the sphere becomes indefinitely small, in the sense that it represents a motion which does not decrease as the velocity of the sphere decreases. It seems unlikely that such a motion would be produced under experimental conditions.

scholarly journals The Stability Conditions for a Heavy Solid Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
A. I. Ismail
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Sufficient Conditions ◽  
The Body ◽  
Stability Conditions ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Necessary And Sufficient

In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z-axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as I 1 < I 2 < I 3 . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

scholarly journals On the oscillation of a nonlinear two-dimensional difference systems

2001 ◽  
Vol 32 (3) ◽  
pp. 201-209 ◽  
Author(s):  
E. Thandapani ◽  
B. Ponnammal
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Real Sequence ◽  
Two Dimensional ◽  
Difference System ◽  
Nonoscillatory Solutions ◽  
Difference Systems ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Strongly Sublinear

The authors consider the two-dimensional difference system$$ \Delta x_n = b_n g (y_n) $$ $$ \Delta y_n = -f(n, x_{n+1}) $$where $ n \in N(n_0) = \{ n_0, n_0+1, \ldots \} $, $ n_0 $ a nonnegative integer; $ \{ b_n \} $ is a real sequence, $ f: N(n_0) \times {\rm R} \to {\rm R} $ is continuous with $ u f(n,u) > 0 $ for all $ u \ne 0 $. Necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior are given. Also sufficient conditions for all solutions to be oscillatory are obtained if $ f $ is either strongly sublinear or strongly superlinear. Examples of their results are also inserted.

Two- and Three-Dimensional Simulations of the Flow Around a Cylinder Fitted With Strakes

2012 ◽  
Author(s):  
Bruno S. Carmo ◽  
Rafael S. Gioria ◽  
Ivan Korkischko ◽  
Cesar M. Freire ◽  
Julio R. Meneghini
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
The Body ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Flow Around A Cylinder ◽  
Three Dimensional Simulations ◽  
Angle Of Rotation

Two- and three-dimensional simulations of the flow around straked cylinders are presented. For the two-dimensional simulations we used the Spectral/hp Element Method, and carried out simulations for five different angles of rotation of the cylinder with respect to the free stream. Fixed and elastically-mounted cylinders were tested, and the Reynolds number was kept constant and equal to 150. The results were compared to those obtained from the simulation of the flow around a bare cylinder under the same conditions. We observed that the two-dimensional strakes are not effective in suppressing the vibration of the cylinders, but also noticed that the responses were completely different even with a slight change in the angle of rotation of the body. The three-dimensional results showed that there are two mechanisms of suppression: the main one is the decrease in the vortex shedding correlation along the span, whilst a secondary one is the vortex wake formation farther downstream.

A Study of Water Surface Deformation Due to Tip Vortices Wing-in-Ground Effect

2007 ◽  
Vol 51 (02) ◽  
pp. 182-186
Author(s):  
Tracie J. Barber
Keyword(s):  
Water Surface ◽  
Surface Deformation ◽  
Three Dimensional ◽  
Ground Effect ◽  
Aerodynamic Performance ◽  
The Body ◽  
Vehicle Design ◽  
Two Dimensional ◽  
Tip Vortices ◽  
Wing Tip

The accurate prediction of ground effect aerodynamics is an important aspect of wing-in-ground (WIG) effect vehicle design. When WIG vehicles operate over water, the deformation of the nonrigid surface beneath the body may affect the aerodynamic performance of the craft. The likely surface deformation has been considered from a theoretical and numerical position. Both two-dimensional and three-dimensional cases have been considered, and results show that any deformation occurring on the water surface is likely to be caused by the wing tip vortices rather than an increased pressure distribution beneath the wing.

On the Integral Extensions of Quadratic Forms Over Local Fields

1970 ◽  
Vol 22 (2) ◽  
pp. 297-307 ◽  
Author(s):  
Melvin Band
Keyword(s):  
Prime Ideal ◽  
Local Field ◽  
Quadratic Forms ◽  
Sufficient Conditions ◽  
Local Fields ◽  
Ring Of Integers ◽  
Finite Dimensional ◽  
Integral Analogue ◽  
Necessary And Sufficient ◽  
Special Case

Let F be a local field with ring of integers and unique prime ideal (p). Suppose that V a finite-dimensional regular quadratic space over F, W and W′ are two isometric subspaces of V (i.e. τ: W → W′ is an isometry from W to W′). By the well-known Witt's Theorem, τ can always be extended to an isometry σ ∈ O(V).The integral analogue of this theorem has been solved over non-dyadic local fields by James and Rosenzweig [2], over the 2-adic fields by Trojan [4], and partially over the dyadics by Hsia [1], all for the special case that W is a line. In this paper we give necessary and sufficient conditions that two arbitrary dimensional subspaces W and W′ are integrally equivalent over non-dyadic local fields.

On Extending Projectives of Finite Group-Graded Algebras

1991 ◽  
Vol 34 (2) ◽  
pp. 224-228
Author(s):  
Morton E. Harris
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Group Representation ◽  
Sufficient Conditions ◽  
Projective Cover ◽  
Graded Algebras ◽  
Finite Dimensional ◽  
Completely Reducible ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractLet G be a finite group, let k be a field and let R be a finite dimensional fully G-graded k-algebra. Also let L be a completely reducible R-module and let P be a projective cover of R. We give necessary and sufficient conditions for P|R1 to be a projective cover of L|R1 in Mod (R1). In particular, this happens if and only if L is R1-projective. Some consequences in finite group representation theory are deduced.

scholarly journals Experience of employment of computational models for water quality modelling

2019 ◽  
Vol 97 ◽  
pp. 05030 ◽  
Author(s):  
Anatoly Krutov ◽  
Dilshod Bazarov ◽  
Begzod Norkulov ◽  
Bakhtiyar Obidov ◽  
Bobur Nazarov
Keyword(s):  
Computational Models ◽  
Numerical Models ◽  
Qualitative Difference ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Aral Sea ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model ◽  
Wind Currents

The purpose of the article is to develop the required and sufficient conditions under which numerical methods can be used for engineering calculations and for scientific research of hydrodynamic processes in solving practical problems related to predicting the spread of pollutants in water bodies and streams. The conducted studies consisted in comparing the results of laboratory experiments and mathematical modelling, in particular the distribution of heat in a stream with different temperature in water layers was studied. To check the adequacy of the proposed numerical models, calculations were performed and comparisons were made with the results of experimental data. The obtained results allowed to determine the boundaries of the qualitative difference in the flow behaviour for different numbers of Froude and Reynolds. The accuracy of the method was also studied. A number of additional requirements for numerical models were proposed in addition to approcsimation and stability, such as requirements of conservativeness (divergence), existence of trivial solutions on grids, possibility to calculate highly unsteady, quasi-stable, pulsating and stationary flows, requirement of invariance of linearized equations, as well as the requirement of a one-dimensional scheme to be a consequence of a two-dimensional scheme. Distribution of velocities of wind currents using a three-dimensional and two-dimensional model was studied for a real object. A shallow-water bay of the Aral Sea was chosen as the object for the research. Comparison of the calculation results for both models showed that the flow velocity fields, as well as the distribution of pollutants in shallow waters, can be performed using a two-dimensional model.

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