On the Relation of the Principle of Maximum Dissipation to the Principles of Jourdain and Gauss for Rigid Body Systems

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Kerim Yunt
Keyword(s):  
Rigid Body ◽  
Potential Theory ◽  
Nonsmooth Analysis ◽  
Mechanical Systems ◽  
Time Dependent ◽  
Necessary Condition ◽  
Definition Of ◽  
Principle Of Maximum ◽  
Variational Condition

A dissipation based definition of the principle of Jourdain is presented for rheonomic (explicitly time dependent) mechanical systems, which evolve under the influence of convex dissipation potentials. It is shown, that the variational condition of the dissipative principle of Jourdain is the necessary condition for the maximization of the total dissipated power with respect to generalized velocities. The principle of maximum dissipation is shown to be the dual principle of the dissipative principle of Jourdain. A dissipative principle of Gauss is formulated by making use of nonsmooth analysis and potential theory and its dual principle is formulated.

Augmented Perpetual Manifolds and Perpetual Mechanical Systems-Part I: Definitions, Theorem and Corollary for Triggering Perpetual Manifolds, Application in Reduced Order Modeling and Particle-Wave Motion of Flexible Mechanical Systems

2021 ◽  
Author(s):  
Fotios Georgiades
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Mechanical Engineering ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Reduced Order ◽  
Rigid Body Motions ◽  
Definition Of ◽  
External Forces ◽  
Perpetual Points

Abstract Perpetual points in mechanical systems defined recently. Herein are used to seek specific types of solutions of N-degrees of freedom systems, and their significance in mechanics is discussed. In discrete linear mechanical systems, is proven, that the perpetual points are forming the perpetual manifolds and they are associated with rigid body motions, and these systems are called perpetual. The definition of perpetual manifolds herein is extended to the augmented perpetual manifolds. A theorem, defining the conditions of the external forces applied in an N-degrees of freedom system lead to a solution in the exact augmented perpetual manifold of rigid body motions, is proven. In this case, the motion by only one differential equation is described, therefore forms reduced-order modelling of the original equations of motion. Further on, a corollary is proven, that in the augmented perpetual manifolds for external harmonic force the system moves in dual mode as wave-particle. The developed theory is certified in three examples and the analytical solutions are in excellent agreement with the numerical simulations. The outcome of this research is significant in several sciences, in mathematics, in physics and in mechanical engineering. In mathematics, this theory is significant for deriving particular solutions of nonlinear systems of differential equations. In physics/mechanics, the existence of wave-particle motion of flexible mechanical systems is of substantial value. Finally in mechanical engineering, the theory in all mechanical structures can be applied, e.g. cars, aeroplanes, spaceships, boats etc. targeting only the rigid body motions.

Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers

1975 ◽  
Vol 42 (3) ◽  
pp. 552-556 ◽  
Author(s):  
A. J. Padgaonkar ◽  
K. W. Krieger ◽  
A. I. King
Keyword(s):  
Experimental Data ◽  
Rigid Body ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Theory And Practice ◽  
Body Segments ◽  
Impact Biomechanics ◽  
The Stability ◽  
Definition Of

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.

scholarly journals SYSTEM AND CYBERNETIC APPROACH TO DEFINITION OF THE CONCEPT “SAFETY”

2015 ◽  
pp. 18-25
Author(s):  
Alexandr Matveev ◽  
Vladimir Matveev
Keyword(s):  
Necessary Condition ◽  
Target Orientation ◽  
Definition Of ◽  
To Receive

The analysis of the existing approaches to definition of the concept “safety” is given. The target orientation in the course of safety is proved. The reasons capable to break safety of the operated systems are established. On the basis of system and cybernetic approach and the formalized principle of systemacity definition of the concept “safety” was received. It is revealed that a necessary condition of safety is predictability of behavior of system in the environment including and other subjects of management, due to the corresponding formation of vectors of opportunities and management of system, allowing to receive the corresponding ratio of existential conditions of system and functioning of system, allowing to reach system of the demanded efficiency indicator level (target mission). It is received that a necessary condition of steady stay of system (object) in the environment is existence of knowledge of this Wednesday, possible options of behavior of system concerning factors of the environment and skills of management of system.

scholarly journals The Approximation of Entropy for Smoluchowski Coagulation Equation With TEMOM

2021 ◽  
Author(s):  
Mingliang Xie
Keyword(s):  
Average Particle ◽  
Particle Volume ◽  
Principle Of Maximum Entropy ◽  
Global Properties ◽  
Smoluchowski Coagulation Equation ◽  
Coagulation Equation ◽  
Definition Of ◽  
Definition Of Information ◽  
Increasing Function ◽  
Principle Of Maximum

In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

A Recommendation for Expanding the Definition of Moral Distress Experienced in the Workplace

2013 ◽  
Vol 6 ◽  
Author(s):  
Monique Frances Crane ◽  
Piers Bayl-Smith ◽  
John Cartmill
Keyword(s):  
Decision Making ◽  
Moral Distress ◽  
Structured Interview ◽  
Institutional Constraints ◽  
Necessary Condition ◽  
Medical Doctors ◽  
Moral Framework ◽  
Definition Of ◽  
Occupational Settings ◽  
Core Problem

Despite the importance of moral distress in the nursing scholarship, little attention is paid to the phenomena in the psychological literature as an important occupational stressor. A factor limiting the application of moral distress to other occupational settings is its definitional features. First, a necessary condition of moral distress is the acknowledgment prior to behaviour initiation that behaviour will contravene personal moral ideals. Second, the definition of moral distress specifies that the inability to act in accordance with one's moral framework is driven by institutional constraints (non-autonomous behaviour). This article proposes that moral distress not be limited in these ways, and makes two central contributions to resolve this core problem. We offer a critique and extension of the conceptual definition of moral distress. Fourteen Australian medical doctors participated in a semi-structured interview regarding occupational morally distressing events. Medical doctors were chosen for our interviews because they are an occupational population with considerable decision-making autonomy. Based on the findings, two recommendations are made: (1) that the definition of moral distress is not limited to events where decision-making and behaviour is non-autonomous, and (2) moral distress should not be limited to occasions where the moral conflict is identified prior to decision-making or behaviour. An alternative definition of moral distress is proposed. We conclude that while organisational limitations are an important precipitate of moral distress, they are not a necessary condition for its emergence.

Application of the Tornado-Like Flow Theory to the Study of Blood Flow in the Heart and Main Vessels: Study of the Potential Swirling Jets Structure in an Arbitrary Viscous Medium

2019 ◽  
Author(s):  
E. Talygin ◽  
G. Kiknadze ◽  
A. Agafonov ◽  
A. Gorodkov
Keyword(s):  
Blood Flow ◽  
Velocity Field ◽  
Analytical Solution ◽  
Coordinate System ◽  
Biologically Active ◽  
Time Dependent ◽  
Characteristic Functions ◽  
Swirling Jet ◽  
Cylindrical Coordinate ◽  
Definition Of

Abstract In previous works it has been proved that the dynamic geometry of the streamlined surface of the flow channel of the heart chambers and main arteries corresponds with a good agreement to the shape of the swirling flow streamlines. The vectorial velocity field of such a flow in a cylindrical coordinate system was described by means of specific analytical solution basing on the potentiality of the longitudinal and radial velocity components. The viscosity of the medium was taken into account only in the expression for the azimuthal velocity component and the significant effect of viscosity was manifested only in a narrow axial region of a swirling jet. The flow described by the above relations is quasipotential, axisymmetric, and convergent. The structural organization of this flow implies the elimination of rupture and stagnation zones, and minimizes the viscous losses. The proximity of the real blood flow under the normal conditions to the specified class of swirling flows allows us to determine the basic properties of the blood flow possessing the high pressure-flow characteristics without stability loss. The blood flow has an external border, and the interaction with the channel wall and between moving fluid elements is weak. These properties of the jet explain the possibility of a balanced blood flow in biologically active boundaries. Violation of the jet properties can lead to the excitation of biologically active components and trigger the corresponding cascade protective and compensatory processes. The evolution of the flow is determined by the time-dependent characteristic functions, which are the frequency characteristics of the rotating jet, as well as functions depending on the dimension of the swirling jet. Previous experimental studies revealed close connection between changes in the characteristic functions and dynamics of the cardiac cycle. Therefore, it is natural to express these functions in analytical form. For these purposes it was necessary to establish the link between these functions and the spatial characteristics of the swirling jet. To solve this problem the analytical solution for the velocity field of a swirling jet was substituted into the Navier-Stokes system and continuity differential equations in a cylindrical coordinate system. As a result, a new system of differential equations was obtained where the characteristic functions could be derived. The solution of these equations allows the identification of time-dependent characteristic functions, and the establishment of a link between the characteristic functions and the spatial coordinates of the swirling jet. This link gives the opportunity to substantiate a theoretical possibility for the modeling of quasipotential viscous flows with a given structure. The definition of characteristic functions makes it possible to obtain the exact solution which allows formalization of the boundary conditions for physical modeling and experimental study of this flow type. Such transformations allow the definition of the conditions supporting renewable swirling blood flow in the transport arterial segment of the circulatory system and provide the basis for new principles of modeling, diagnosis and surgical treatment of circulatory disorders associated with the changes in geometry of the heart and great vessels.

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