The Top With a Blunted Vertex Slipping With Light Friction at a High Rate of Spin

1999 ◽  
Vol 67 (3) ◽  
pp. 616-618
Author(s):  
P. C. Paris, ◽  
L. Zhang, and ◽  
H. Tada
Keyword(s):  
Angular Momentum ◽  
Complex Analysis ◽  
Sliding Friction ◽  
Steady Motion ◽  
Rate Of Change ◽  
High Rate ◽  
Lagrange’S Equations ◽  
The Coefficient Of Friction ◽  
Lagrange's Equations ◽  
Simple Approximate Solution

The problem of determining the motion of a top is a classic example of a complex analysis in analytical dynamics. Adding a blunt tip to the top and setting it spinning on a surface with sliding friction might be thought to render it intractable for simple analysis. However, if it is set in motion with a high rate of spin it is possible to find a simple approximate solution for the case of approximate steady precession. For this pseudo-steady motion it will be noted that the rate of diminution of the nutation will also be almost constant. Further, the ratio of these rates (latter over former) will be equal to the negative of the coefficient of friction for the top slipping on the surface. As a consequence the mass center of the top will tend to proceed around a steady circle above the plane. These results will first be observed by writing the full Lagrange’s equations for the problem and reducing them prior to integration by observing appropriate approximations by deleting relatively smaller terms. The above results will then follow directly. Further, the full Lagrange’s equations will be numerically integrated to show that the analytically developed approximate results are appropriate. Once these results are known, it is observed that a subsequent intuitive analysis based on time rate of change of angular momentum leads to the same results, if only the angular momentum about the spin axis is considered with other relevant assumptions. [S0021-8936(00)00203-8]

scholarly journals Insulation Life Span of Low-Voltage Electric Motors—A Survey

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1738
Author(s):  
Vanessa Neves Höpner ◽  
Volmir Eugênio Wilhelm
Keyword(s):  
Life Span ◽  
Electric Motor ◽  
Low Voltage ◽  
Frequency Converter ◽  
Rate Of Change ◽  
High Rate ◽  
Switching Frequency ◽  
Electric Motors ◽  
Frequency Converters ◽  
High Switching Frequency

The use of static frequency converters, which have a high switching frequency, generates voltage pulses with a high rate of change over time. In combination with cable and motor impedance, this generates repetitive overvoltage at the motor terminals, influencing the occurrence of partial discharges between conductors, causing degradation of the insulation of electric motors. Understanding the effects resulting from the frequency converter–electric motor interaction is essential for developing and implementing insulation systems with characteristics that support the most diverse applications, have an operating life under economically viable conditions, and promote energy efficiency. With this objective, a search was carried out in three recognized databases. Duplicate articles were eliminated, resulting in 1069 articles, which were systematically categorized and reviewed, resulting in 481 articles discussing the causes of degradation in the insulation of electric motors powered by frequency converters. A bibliographic portfolio was built and evaluated, with 230 articles that present results on the factors that can be used in estimating the life span of electric motor insulation. In this structure, the historical evolution of the collected information, the authors who conducted the most research on the theme, and the relevance of the knowledge presented in the works were considered.

scholarly journals Numerical Modeling of the Motion of the Flat Textile Structures

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Piotr Szablewski
Keyword(s):  
Numerical Modeling ◽  
Boundary Conditions ◽  
Discrete Model ◽  
Gravity Force ◽  
Dynamic Conditions ◽  
Textile Structure ◽  
Sewing Thread ◽  
Lagrange’S Equations ◽  
Lagrange's Equations ◽  
Time Boundary

In many problems from the field of textile engineering (e.g., fabric folding, motion of the sewing thread) it is necessary to investigate the motion of the objects in dynamic conditions, taking into consideration the influence of the forces of inertia and changing in the time boundary conditions. This paper deals with the model analysis of the motion of the flat textile structure using Lagrange's equations in two variants: without constraints and with constraints. The motion of the objects is under the influence of the gravity force. Lagrange's equations have been used for discrete model of the structure.

scholarly journals IV. On some applications of dynamical principles to physical phenomena

1885 ◽  
Vol 176 ◽  
pp. 307-342 ◽  
Keyword(s):  
Physical Phenomenon ◽  
Good Deal ◽  
Rigid Bodies ◽  
Great Success ◽  
Material System ◽  
Electric Currents ◽  
Conservation Of Energy ◽  
Lagrange’S Equations ◽  
Physical Phenomena ◽  
Lagrange's Equations

1. The tendency to apply dynamical principles and methods to explain physical phenomena has steadily increased ever since the discovery of the principle of the Conservation of Energy. This discovery called attention to the ready conversion of the energy of visible motion into such apparently dissimilar things as heat and electric currents, and led almost irresistibly to the conclusion that these too are forms of kinetic energy, though the moving bodies must be infinitesimally small in comparison with the bodies which form the moving pieces of any of the structures or machines with which we are acquainted. As soon as this conception of heat and electricity was reached mathematicians began to apply to them the dynamical method of the Con­servation of Energy, and many physical phenomena were shown to be related to each other, and others predicted by the use of this principle; thus, to take an example, the induction of electric currents by a moving magnet was shown by von Helmholtz to be a necessary consequence of the fact that an electric current produces a magnetic field. Of late years things have been carried still further; thus Sir William Thomson in many of his later papers, and especially in his address to the British Association at Montreal on “Steps towards a Kinetic Theory of Matter,” has devoted a good deal of attention to the description of machines capable of producing effects analogous to some physical phenomenon, such, for example, as the rotation of the plane of polarisation of light by quartz and other crystals. For these reasons the view (which we owe to the principle of the Conservation of Energy) that every physical phenomenon admits of a dynamical explanation is one that will hardly be questioned at the present time. We may look on the matter (including, if necessary, the ether) which plays a part in any physical phenomenon as forming a material system and study the dynamics of this system by means of any of the methods which we apply to the ordinary systems in the Dynamics of Rigid Bodies. As we do not know much about the structure of the systems we can only hope to obtain useful results by using methods which do not require an exact knowledge of the mechanism of the system. The method of the Conservation of Energy is such a method, but there are others which hardly require a greater knowledge of the structure of the system and yet are capable of giving us more definite information than that principle when used in the ordinary way. Lagrange's equations and Hamilton's method of Varying Action are methods of this kind, and it is the object of this paper to apply these methods to study the transformations of some of the forms of energy, and to show how useful they are for coordinating results of very different kinds as well as for suggesting new phenomena. A good many of the results which we shall get have been or can be got by the use of the ordinary principle of Thermodynamics, and it is obvious that this principle must have close relations with any method based on considerations about energy. Lagrange’s equations were used with great success by Maxwell in his ‘Treatise on Electricity and Magnetism,’ vol. ii., chaps. 6, 7, 8, to find the equations of the electromagnetic field.

scholarly journals Growing bubbles rising in line

2001 ◽  
Vol 5 (2) ◽  
pp. 65-73 ◽  
Author(s):  
John F. Harper
Keyword(s):  
Reynolds Numbers ◽  
Dissipation Function ◽  
Supersaturated Solution ◽  
Liquid Theory ◽  
High Reynolds Numbers ◽  
Lagrange’S Equations ◽  
Spherical Bubbles ◽  
High Reynolds ◽  
Lagrange's Equations

Over many years the author and others have given theories for bubbles rising in line in a liquid. Theory has usually suggested that the bubbles will tend towards a stable distance apart, but experiments have often showed them pairing off and sometimes coalescing. However, existing theory seems not to deal adequately with the case of bubbles growing as they rise, which they do if the liquid is boiling, or is a supersaturated solution of a gas, or simply because the pressure decreases with height. That omission is now addressed, for spherical bubbles rising at high Reynolds numbers. As the flow is then nearly irrotational, Lagrange's equations can be used with Rayleigh's dissipation function. The theory also works for bubbles shrinking as they rise because they dissolve.

scholarly journals Solid Lubrication by Multiwalled Carbon Nanotubes in Air and in Vacuum for Space and Aeronautics Applications

2005 ◽  
Author(s):  
K. Miyoshi ◽  
K. W. Street ◽  
R. L. Vander Wal ◽  
R. Andrews ◽  
David Jacques ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Multiwalled Carbon Nanotubes ◽  
Coefficient Of Friction ◽  
Sliding Friction ◽  
Solid Lubrication ◽  
Multiwalled Carbon ◽  
Solid Lubrication Friction ◽  
The Coefficient Of Friction ◽  
Dry Conditions ◽  
Steel Balls

To evaluate recently developed aligned multiwalled carbon nanotubes (MWNTs) and dispersed MWNTs for solid lubrication applications, unidirectional sliding friction experiments were conducted with 440C stainless steel balls and hemispherical alumina-yttria stabilized zirconia pins in sliding contact with the MWNTs deposited on quartz disks in air and in vacuum. The results indicate that MWNTs have superior solid lubrication friction properties and endurance lives in air and vacuum under dry conditions. The coefficient of friction of the dispersed MWNTs is close to 0.05 and 0.009 in air and in vacuum, respectively, showing good dry lubricating ability. The wear life of MWNTs exceeds 1 million passes in both air and vacuum showing good durability. In general, the low coefficient of friction can be attributed to the combination of the transferred, agglomerated patches of MWNTs on the counterpart ball or pin surfaces and the presence of tubular MWNTs at interfaces.

scholarly journals Development and evaluation of the focused assessment of sonographic pathologies in the intensive care unit (FASP-ICU) protocol

Critical Care ◽  
2021 ◽  
Vol 25 (1) ◽  
Author(s):  
Stefan Schmidt ◽  
Jana-Katharina Dieks ◽  
Michael Quintel ◽  
Onnen Moerer
Keyword(s):  
Intensive Care Unit ◽  
Intensive Care ◽  
Conclusive Evidence ◽  
Rate Of Change ◽  
University Hospital ◽  
High Rate ◽  
Whole Body ◽  
Routine Surveillance ◽  
Organ Systems ◽  
Training Schemes

Abstract Background The use of ultrasonography in the intensive care unit (ICU) is steadily increasing but is usually restricted to examinations of single organs or organ systems. In this study, we combine the ultrasound approaches the most relevant to ICU to design a whole-body ultrasound (WBU) protocol. Recommendations and training schemes for WBU are sparse and lack conclusive evidence. Our aim was therefore to define the range and prevalence of abnormalities detectable by WBU to develop a simple and fast bedside examination protocol, and to evaluate the value of routine surveillance WBU in ICU patients. Methods A protocol for focused assessments of sonographic abnormalities of the ocular, vascular, pulmonary, cardiac and abdominal systems was developed to evaluate 99 predefined sonographic entities on the day of admission and on days 3, 6, 10 and 15 of the ICU admission. The study was a clinical prospective single-center trial in 111 consecutive patients admitted to the surgical ICUs of a tertiary university hospital. Results A total of 3003 abnormalities demonstrable by sonography were detected in 1275 individual scans of organ systems and 4395 individual single-organ examinations. The rate of previously undetected abnormalities ranged from 6.4 ± 4.2 on the day of admission to 2.9 ± 1.8 on day 15. Based on the sonographic findings, intensive care therapy was altered following 45.1% of examinations. Mean examination time was 18.7 ± 3.2 min, or 1.6 invested minutes per detected abnormality. Conclusions Performing the WBU protocol led to therapy changes in 45.1% of the time. Detected sonographic abnormalities showed a high rate of change in the course of the serial assessments, underlining the value of routine ultrasound examinations in the ICU. Trial registration The study was registered in the German Clinical Trials Register (DRKS, 7 April 2017; retrospectively registered) under the identifier DRKS00010428.

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