The Mathematical Theory of the Snaking of Two-wheeled Trailers, with Practical Rules and Devices for Preventing Snaking

1951 ◽  
Vol 5 (1) ◽  
pp. 175-190 ◽  
Author(s):  
D. Williams
Keyword(s):  
General Solution ◽  
Detailed Analysis ◽  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Degrees Of Freedom ◽  
Critical Speed ◽  
Elastic System ◽  
Practical Experience ◽  
Dynamical Equations ◽  
All Speeds

It is well known that a prime essential in bringing about unstable motion in any elastic system is the presence of at least two degrees of freedom. A trailer and its towing vehicle constitute a mechanical system with a number of degrees of freedom, and a main feature of the present problem is the necessity for deciding which are essential factors in the unstable motion and which are trivial or merely incidental. The idea of including all the possible degrees of freedom in the dynamical equations, thereby obtaining a general solution in which the part played by the several parameters can be seen, is quite impracticable. In Part I of the paper the results obtained from the mathematical analysis of the problem are given and discussed. There is a general agreement with practical experience. Part II contains the detailed analysis on which the conclusions in Part I are based. It is emphasized that the main purpose of the analysis is not to enable calculations to be made of the precise critical speed at which snaking begins for any particular combination of tractor and trailer, but to discover what factors make for stability and for instability, and how to design for immunity from snaking at all speeds.

Mathematical Analysis on Helicoids Architectural Form

2013 ◽  
Vol 790 ◽  
pp. 273-277
Author(s):  
Zhong Yi ◽  
Cheng Zhi Yuan
Keyword(s):  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Architecture Design ◽  
Curved Surfaces ◽  
Mathematical Transformation ◽  
Geometric Figure ◽  
Topological Transformation ◽  
Architectural Form ◽  
Geometric Figures ◽  
Architecture Modeling

In a sense, architecture may be called as a geometric figure. Although architectural forms are very different, the form from one kind of architecture to another kind of architecture is equivalent to one kind of mathematical transformation in view of mathematics; for example, the transformation between a cube architecture and a spherical architecture belongs to a topological transformation. Currently, many sculptural features appear in the architecture design, which may be called as the nonlinear architecture. Curves and curved surfaces are widely used in the architecture modeling. Moreover, functional spaces are divided inside the architecture shell according to requirements. Architects are inclined to use a mathematical theory especially the geometrical knowledge in an architecture design. However, architects can not imagine many artistic geometric figures in geometry. Besides, such wonderful geometric figures always include some miraculous mathematical and physical properties.

scholarly journals Vibration Analysis by the Wigner-Ville Transformation Method

2018 ◽  
Vol 20 (4) ◽  
pp. 24-28 ◽  
Author(s):  
Jaroslav Smutny ◽  
Viktor Nohal ◽  
Daniela Vukusicova ◽  
Herbert Seelmann
Keyword(s):  
Mathematical Analysis ◽  
Vibration Analysis ◽  
Linear Time ◽  
Practical Experience ◽  
Transformation Method ◽  
Application Area ◽  
Interesting Application ◽  
Time Frequency ◽  
Natural Processes

This paper deals with description and application of the Wigner-Ville transformation for vibration analysis. This transformation belongs to the group of non-linear time-frequency processes. Thanks to its properties, it may be successfully used in the area of non-stationary and transitional signals describing various natural processes. The use in the field of the railway constructions testing represents a quite an interesting application area of the transformation. This paper contains mathematical analysis of the transformation, a case study and practical experience obtained and recommendations for its practical use.

scholarly journals Wormholes in Wyman's solution

2014 ◽  
Vol 23 (11) ◽  
pp. 1450086 ◽  
Author(s):  
J. B. Formiga ◽  
T. S. Almeida
Keyword(s):  
Scalar Field ◽  
General Solution ◽  
Detailed Analysis ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Human Beings ◽  
Einstein Field Equations ◽  
Field Equations

The most general solution of the Einstein field equations coupled with a massless scalar field is known as Wyman's solution. This solution is also present in the Brans–Dicke theory and, due to its importance, it has been studied in detail by many authors. However, this solutions has not been studied from the perspective of a possible wormhole. In this paper, we perform a detailed analysis of this issue. It turns out that there is a wormhole. Although we prove that the so-called throat cannot be traversed by human beings, it can be traversed by particles and bodies that can last long enough.

Modelling and evaluation of the hunting behaviour of a high-speed railway vehicle on curved track

2018 ◽  
Vol 233 (2) ◽  
pp. 220-236 ◽  
Author(s):  
Vivek Kumar ◽  
Vikas Rastogi ◽  
PM Pathak
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Critical Speed ◽  
Transportation Network ◽  
Graph Model ◽  
Railway Vehicle ◽  
Physical Damage ◽  
Creep Theory ◽  
High Speed Railway ◽  
Hunting Behaviour

Nowadays, rail transport is a very important part of the transportation network for any countries. The demand for high operational speed makes hunting a very common instability problem in railway vehicles. Hunting leads to discomfort and causes physical damage to carriage components, such as wheels, rails, etc. The causes of instability and derailment should be identified and eliminated at the designing stage of a train to ensure its safe operation. In most of the earlier studies on hunting behaviour, a simplified model with a lower degree of freedom were considered, which resulted in incorrect results in some instances. In this study, a complete bond graph model of a railway vehicle with 31 degrees of freedom is presented to determine the response of a high-speed railway vehicle. For this purpose, two wheel–rail contacts grounded on a flange contact and Kalker’s linear creep theory are implemented. The model is simulated to observe the effects of suspension elements on the vehicle’s critical hunting velocity. It is observed that the critical hunting speed is extremely sensitive to the primary longitudinal and lateral springs. Other primary and secondary springs and dampers also affect the critical speed to some extent. However, the critical hunting velocity is insensitive to vertical suspension elements for both the primary and secondary suspensions. Also, the critical speed is found to be inversely related to the conicity of the wheel.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

Reviews - A. E. Heath. Preface. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 7–8. - R. Rhees. Note in editing. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 9–43. - George Boole. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. A reprint of 191. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 45–119. - George Boole. Later notes (to the foregoing). Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 119–124. (Taken from manuscript in the Library of the Royal Society.) - George Boole. The calculus of logic. A reprint of 192. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 125–140. - George Boole. Sketch of a theory and method of probabilities founded upon the calculus of logic. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 141–166. (From manuscripts in the Royal Society Library, probably before 1851.) - George Boole. Of propositions numerically definite. A reprint of 194. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 167–186. - George Boole. The claims of science, especially as founded in its relation to human nature. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 187–210. (Lecture published in London, 1851.) - George Boole. Logic and reasoning. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 211–229. (From Royal Society manuscripts, after 1855.) - George Boole. Extracts from a paper entitled “On the mathematical theory of logic and on the philosophical interpretation of its methods and processes.”Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 230–246. (From Royal Society manuscripts, later than 1855.)

1959 ◽  
Vol 24 (3) ◽  
pp. 203-209 ◽  
Author(s):  
Michael Dummett
Keyword(s):  
Mathematical Analysis ◽  
Royal Society ◽  
Mathematical Theory ◽  
Deductive Reasoning ◽  
Publishing Company ◽  
Philosophical Interpretation ◽  
Open Court ◽  
Court Publishing ◽  
George Boole ◽  
Nature Studies

Phase transitions in the adsorbed molecular chains

Open Physics ◽  
2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Victor Lykah ◽  
Evgen Syrkin
Keyword(s):  
Effective Potential ◽  
Degrees Of Freedom ◽  
Nearest Neighbor ◽  
Structural Data ◽  
Dynamical Analysis ◽  
Second Phase ◽  
Integral Of Motion ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Wave Limit

AbstractRotational excitations of molecular adsorbed layers are studied theoretically. Nonlinear dynamical equations are obtained with accounting of quadrupolar interactions between molecules and freezing of translational degrees of freedom. The equilibrium positions of the molecules are found to be experimentally observed structures with alternating rotational ordering of planar rotors along the direction to the nearest neighbor (for linear or square structures) under low temperature. Dynamical analysis gives an integral of motion (energy) of the chain that in the long-wave limit leads consequently to the existence of four phases. The first one corresponds to oscillations near equilibrium ordered states. The second phase corresponds to low-energy rotational excitations along ‘valleys’ (easy directions in the effective potential) that do not destroy strong correlations between molecules while structural data can show rotational disorder (melting). The third phase corresponds to an energy that is enough to travel between ‘valleys’; only some ‘islands’ in the angle space are forbidden. Complete destruction of correlation when the energy is over the peaks of the effective potential corresponds to the fourth phase. Therefore rotational melting is a complex phenomenon that has several stages.

scholarly journals IMPROVEMENT OF TRAINING LOADS AIMED TO DEVELOP THE STRUCTURE OF FUNCTIONAL SUPPORT FOR SPECIAL WORKING CAPACITY AMONG QUALIFIED KAYAKERS

2021 ◽  
Vol 5 (1) ◽  
pp. 104-116
Author(s):  
Olga Rusanova ◽  
Andrii Diachenko ◽  
Zijian Huang ◽  
Xueyan Gao
Keyword(s):  
Detailed Analysis ◽  
Research Methods ◽  
Energy Supply ◽  
Practical Experience ◽  
Gas Analysis ◽  
Working Capacity ◽  
Cardiorespiratory System ◽  
Biochemical Research ◽  
Special Working ◽  
Functional Support

Introduction. Despite the fact that currently theorists have systematized some aspects of scientific knowledge to increase the efficiency of functional support of special performance of rowers, while the formation of prerequisites for improving the training load of qualified athletes aged 16-17 in kayaking and canoeing has not been the subject of special research. This leads to the isolation of the problematic issue that needs to be studied and analyzed. Aim is to analyze the structure of functional support of special working capacity and to form preconditions for improving the training loads of qualified athletes aged 16-17, who specialize in kayaking and canoeing. Material and methods: analysis and generalization of data of scientific and methodical literature sources and the Internet, pedagogical observations and natural pedagogical experiment, instrumental research methods using ergometry, gas analysis, pulsometry, biochemical research methods; methods of mathematical statistics. Results. To optimize the system for assessing the functional support of special performance, a set of indicators was selected that integrally reflect the level of functionality of kayakers. Their assessment is the basis for a more detailed analysis of the structure of the functional support of the special capacity of kayakers 16-17 year old . A more detailed analysis is performed with reduced indicators of cattle capacity and aerobic energy supply, as well as performance. As a rule, it is carried out individually and is aimed at studying the cause of the reduced level of certain indicators. In the course of the research the available material on the problems of control, estimation and interpretation of the most informative and integral indicators of reactions of the cardiorespiratory system (CRS) and energy supply of work is systematized; special working capacity of athletes – kayakers. Conclusion. The presented test results (average-statistical and model values of indicators) showed new possibilities of estimation and interpretation of indicators of functional support of special working capacity of qualified athletes aged 16-17, who specialize in kayaking and canoeing. Systematization of data from special literature and practical experience allowed to establish the prerequisites for improving training loads aimed at forming the structure of functional support for special performance of qualified kayakers, and to identify five groups of exercises.

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