Jurr Get to Know Us. This is called outer orientation of the dual time instant. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories. Of the factors which compose it [energy], one is referred to unit of length, and the other to unit of area. English Choose a language for shopping. The Mathematical Structure of Classical and Relativistic Physics : Enzo Tonti : Considering now the middle instants of each time interval we have a second cell complex in time.

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This is called outer orientation of the dual time intervals. Physics, compared to other natural sciences, has the great privilege of considering the quantitative attributes of physical systems and from these originate the physical quantitieswhich can be scalarsvectorstensorsetc.

The third category, that of energy variablesis created by multiplying a configuration variable by a source variable. This gives what I regard as a very important distinction among vector quantities.

Dispatched from the UK in 3 business days When will my order arrive? The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation.

The specific problem is: Since we also need space elements with outer orientation, it is expedient to consider the dual complexobtained by joining the centroids of the cells belonging to the primal complex.

Please discuss further on the talk page. A cell complex and its dual constitute a valid framework to describe the association of physical variables with the oriented space elements. Similar authors to follow June Learn how and when to remove this template message. February Learn how and when to remove this template message. Heterogeneous Media Konstantin Markov. This is evident if we think that we can perform the rates of the first two variables obtaining velocity and force respectively, toni we cannot perform the rates of the last two variables.

The right column includes those physical variables associated with the dual cell complex, whose elements tont endowed with outer orientation: The fundamental problem of a field tont finding the configuration of the field at every time instant, given the spatial distribution and the intensity of its sources which is to say: Each field has its sources for example, electric charges are the source of electric fields, heat generators are the source of thermal fields and forces are the source of motion and deformation: A major contributor to this article appears to have a close connection with its subject.

International Journal of Engineering Science 22, Lastly all potentials e. The classification stems from the observation that each physical variable has a well-defined association with a space and a time element, as shown in Fig.

This article is an orphanas no other articles link to it. Istituto di matematica del Politecnico di Milano Therefore, a displacement is associated with a time interval Twhereas a position vector is associated with a time instant I. Please help improve it to make it understandable to non-expertswithout removing the technical details. Please introduce links to this page from related articles ; try the Find link tool for suggestions.

Available to ship in days. Integral variables are global variables, but there are also global variables which are associated with points, and which, therefore, cannot be considered integral variables. This distinction leads to a classification of physical variables based on their association with space elements.

Tonti diagram Referring here to particle dynamics, we see that configuration variables are geometrical and kinematic variables, while source variables are static and dynamic variables. A General Classification Diagram. Check out the top books of the year on our page Best Books of The very fact that we create volume, surface snzo line densities highlights that the corresponding global variables are associated with volumes, surfaces and lines.

Provide feedback about this page. Amazon Drive Cloud storage from Amazon. A systematic approach to the search for variational principles E Tonti International Conference on Variational Principles in Engineering, 1. Pressure is the ratio of the normal force on an element of plane surface to the surface area, therefore the normal force is the global variable and the pressure is its surface density.

Physical quantities Nezo modeling Applied mathematics Diagrams Classification systems. The algebraic-topological structure of physical theories E Tont Symmetry, similarity and group theoretic methods in mechanics, The cell method E Tonti.

The term space-global variables refers to all physical variables that are not densities of other variables. The mathematical treatment of physics also customarily considers the limit of this ratio to obtain a pointwise density, i. Related Articles

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## Enzo Tonti

Historical note[ edit ] The starting point of this classification stems from a remark by Maxwell. Speaking about analogies in different physical theories, Maxwell wrote in [2] Of the factors which compose it [energy], one is referred to unit of length, and the other to unit of area. This gives what I regard as a very important distinction among vector quantities. This remark leads us to a distinction between vectors referred to lines and vectors referred to surfaces. This is not customarily considered in vector calculus or in physics. In electromagnetism, hence, vectors E and H are associated with lines, and vectors D and B are associated with surfaces. This distinction leads to a classification of physical variables based on their association with space elements.

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