CENTRIFUGAL IMPULSE AS COORDINATE IN THE TABARROKIAN FORMULATION

1995 ◽  
Vol 19 (3) ◽  
pp. 261-269
Author(s):  
F.P.J. Rimrott ◽  
W.M. Szczygielski
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Centrifugal Force ◽  
Nonholonomic Constraint ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Essential Elements ◽  
Model System ◽  
The Other ◽  
Generalized Displacements

While the well-known conventional Lagrange equation, based on kinetic coenergy and potential energy, uses generalized displacements of the inertia (mass) elements of a system as coordinates, the complementary alternative or Tabarrok formulation, is based on kinetic energy and potential coenergy, and uses as coordinates the generalized impulses of the system’s force (spring) elements. A model system specifically selected to be as simple as possible, yet to contain all essential elements for an illustration of the application of the Tabarrokian approach for the case where a centrifugal force is present, has been devised to show that the centrifugal impulse appears as additional coordinate for the complementary Lagrangian, and that the system turns out to be non-Tabarrokian. It is then shown that the centrifugal impulse is related to the other impulse coordinates by a nonholonomic constraint. Eventually the compatibility equations of motion for the model system are obtained.

DISPLACEMENT-IMPULSE COMPLEMENTARY IN ANALYTICAL MECHANICS

1994 ◽  
Vol 18 (3) ◽  
pp. 225-247
Author(s):  
F.P.J. Rimrott ◽  
B. Tabarrok ◽  
J. Altenbach
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Mechanical System ◽  
Equations Of Motion ◽  
Linear Momentum ◽  
Analytical Mechanics ◽  
Translatory Motion ◽  
Generalized Displacements ◽  
Energy Aspects

Based on Euler’s linear momentum law, equations of motion of a mechanical system, consisting of a collection of point masses and force elements, such as springs or dashpots, are derived using generalized impulses, rather than generalized displacements, as coordinates. There are limitations to this approach involving both potential energy aspects and kinetic energy aspects. The present paper if of introductory nature and restricted to systems with translatory motion.

scholarly journals An Analysis of the Energetics of Tropical and Extra-Tropical Regions for Warm ENSO Composite Episodes

2017 ◽  
Vol 32 (1) ◽  
pp. 39-51
Author(s):  
Zayra Christine Sátyro ◽  
José Veiga
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
El Niño ◽  
Energy Production ◽  
El Nino ◽  
Southern Oscillation ◽  
Stable Condition ◽  
The Other ◽  
Tropical Regions ◽  
Using Data

Abstract This study focuses on the quantification and evaluation of the effects of ENSO (El Niño Southern Oscillation) warm phases, using a composite of five intense El Niño episodes between 1979 – 2011 on the Energetic Lorenz Cycle for four distinct regions around the globe: 80° S – 5° N (region 1), 50° S – 5° N (region 2), 30° S – 5° N (region 3), and 30° S – 30° N (region 4), using Data from NCEP reanalysis-II. Briefly, the results showed that zonal terms of potential energy and kinetic energy were intensified, except for region 1, where zonal kinetic energy weakened. Through the analysis of the period in which higher energy production is observed, a strong communication between the available zonal potential and the zonal kinetic energy reservoirs can be identified. This communication weakened the modes linked to eddies of potential energy and kinetic energy, as well as in the other two baroclinic conversions terms. Furthermore, the results indicate that for all the regions, the system itself works to regain its stable condition.

Bond Graphs for Nonholonomic Dynamic Systems

1976 ◽  
Vol 98 (4) ◽  
pp. 361-366 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Dynamic Systems ◽  
Broad Class ◽  
Nonholonomic Systems ◽  
The Other ◽  
Bond Graphs ◽  
Generalized Potential ◽  
Engineering Significance ◽  
Nonholonomic Dynamic Systems

Two very different dynamic systems, one holonomic and the other nonholonomic, can have identical expressions for generalized kinetic energy, generalized potential energy, and transformational constraints between the generalized velocities, and therefore might be confused. Bond graphs for a broad class of nonholonomic systems are shown to differ from their holonomic counterparts simply by the deletion of certain gyrators. Simple examples suggest the engineering significance of nonholonomic systems.

New Approach to the Dynamic Modeling of Compliant Mechanisms

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Wenjing Wang ◽  
Yueqing Yu
Keyword(s):  
Numerical Methods ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Compliant Mechanisms ◽  
Lagrange Equation ◽  
New Approach ◽  
Body Model ◽  
Rigid Body Model

A new dynamic model of compliant mechanisms is developed based on the pseudo-rigid-body model. The kinetic energy and potential energy of various kinds of compliant segments are derived using numerical methods at first. The dynamic equation of planar compliant mechanisms is then developed based on the Lagrange equation. The natural frequency is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the advantage of the proposed method for the dynamic analysis of compliant mechanisms.

Dependence of the joint configuration on the dynamic immobility fulcrum

2019 ◽  
pp. 108-114
Author(s):  
A. D. Kozlov ◽  
Yu. P. Potekhina
Keyword(s):  
Kinetic Energy ◽  
Convex Surface ◽  
The Other ◽  
Concave Surface ◽  
Joint Configuration ◽  
Articular Surfaces

Although joints with synovial cavities and articular surfaces are very variable, they all have one common peculiarity. In most cases, one of the articular surfaces is concave, whereas the other one is convex. During the formation of a joint, the epiphysis, which has less kinetic energy during the movements in the joint, forms a convex surface, whereas large kinetic energy forms the epiphysis with a concave surface. Basing on this concept, the analysis of the structure of the joints, allows to determine forces involved into their formation, and to identify the general patterns of the formation of the skeleton.

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

scholarly journals Heritage Artefacts in the COVID-19 Era: The Aura and Authenticity of 3D Models

2021 ◽  
Vol 7 (1) ◽  
pp. 519-539
Author(s):  
Thiago Minete Cardozo ◽  
Costas Papadopoulos
Keyword(s):  
User Experience ◽  
Three Dimensional ◽  
3D Models ◽  
Essential Elements ◽  
The Other ◽  
Social Distancing ◽  
The Public ◽  
Affective Experiences ◽  
The One ◽  
Digital Engagement

Abstract Museums have been increasingly investing in their digital presence. This became more pressing during the COVID-19 pandemic since heritage institutions had, on the one hand, to temporarily close their doors to visitors while, on the other, find ways to communicate their collections to the public. Virtual tours, revamped websites, and 3D models of cultural artefacts were only a few of the means that museums devised to create alternative ways of digital engagement and counteract the physical and social distancing measures. Although 3D models and collections provide novel ways to interact, visualise, and comprehend the materiality and sensoriality of physical objects, their mediation in digital forms misses essential elements that contribute to (virtual) visitor/user experience. This article explores three-dimensional digitisations of museum artefacts, particularly problematising their aura and authenticity in comparison to their physical counterparts. Building on several studies that have problematised these two concepts, this article establishes an exploratory framework aimed at evaluating the experience of aura and authenticity in 3D digitisations. This exploration allowed us to conclude that even though some aspects of aura and authenticity are intrinsically related to the physicality and materiality of the original, 3D models can still manifest aura and authenticity, as long as a series of parameters, including multimodal contextualisation, interactivity, and affective experiences are facilitated.

scholarly journals The spectrum of thallium fluoride

1937 ◽  
Vol 160 (901) ◽  
pp. 242-253 ◽  
Keyword(s):  
Absorption Spectrum ◽  
Kinetic Energy ◽  
The Other ◽  
Molecular Spectra ◽  
Absorption Tube ◽  
Saturated Vapour ◽  
Long Wave ◽  
Original Investigation ◽  
Wave Edge

This study of the thallium fluoride spectrum was undertaken as part of a detailed investigation into the molecular spectra of the series of heavy diatomic fluorides HgF, TlF, PbF and BiF. Whereas the spectra of PbF (Rochester 1936) and BiF (Howell 1936), of which analyses have already been published, contain no very unusual features the TlF spectrum is particularly rich in them, so that it has seemed desirable to extend the original investigation in order to include the other halides of thallium. The absorption spectrum of the fluoride has already been examined by Boizova and Butkow (1936), their findings being summarized below: 1— A continuum at 2200 A appears when the absorption tube is at a temperature of 155° C. Its long-wave edge moves towards the red with increase of temperature, being at 2700 for the unsaturated vapour and at 3400 for the saturated vapour when the temperature is 280° C. They attributed this continuum to the dissociation of Tl 2 F 2 . Tl 2 F 2 → 2TlF + kinetic energy.

MULTI–INERT OSCILLATORY MECHANISM

2020 ◽  
Vol 2 ◽  
pp. 19-25
Author(s):  
I.P. POPOV
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Oscillation Frequency ◽  
Free Oscillation ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Harmonic Oscillations ◽  
Oscillatory Systems ◽  
Oscillatory Mechanism ◽  
Mutual Conversion

A mechanical oscillatory system with homogeneous elements, namely, with n massive loads (multi– inert oscillator), is considered. The possibility of the appearance of free harmonic oscillations of loads in such a system is shown. Unlike the classical spring pendulum, the oscillations of which are due to the mutual conversion of the kinetic energy of the load into the potential energy of the spring, in a multi–inert oscillator, the oscillations are due to the mutual conversion of only the kinetic energies of the goods. In this case, the acceleration of some loads occurs due to the braking of others. A feature of the multi–inert oscillator is that its free oscillation frequency is not fixed and is determined mainly by the initial conditions. This feature can be very useful for technical applications, for example, for self–neutralization of mechanical reactive (inertial) power in oscillatory systems.

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