The Mathematical Structure of Classical and Relativistic Physics (Modeling and Simulation in Science, Engineering and Technology) Sep 07, by Enzo. Enzo Tonti is on Facebook. Join Facebook to connect with Enzo Tonti and others you may know. Facebook gives people the power to share and makes the. The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram. Enzo Tonti. from: $ Top of Page. My Account ยท Billing.

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The Mathematical Structure of Classical and Relativistic Physics : Enzo Tonti :

The strain of a bar is the ratio of the elongation to its original length, elongation being the global variable and strain the line density. The same classification applies to time elements, i. In this classification, the orientation of the space elements has a fundamental role. It may require cleanup to comply with Wikipedia’s content policies, toni neutral point of view.

On the formal structure of tpnti theories E Tonti 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.

This article has multiple issues. The vertices represent points, the edges lines, the faces surfaces and the cells themselves volumes. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable tontk 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 theories toni are: The physical variables, both global variables and densities, in turn, can be divided into three classes: By the term “space elements” we intend pointslinessurfaces and volumeswhich are denoted PLS and V respectively.

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Amazon Rapids Fun stories for kids on the go. Verified email at units. Book ratings by Goodreads. Title Cited by Year A direct discrete formulation of field laws: Of the factors which compose it [energy], one is referred to unit of length, and the other to unit of area.

Relevant discussion may be found on the talk page. Each of these elements can be given an inner orientation. Figures 3 and 4 show how the space elements of the primal complex, which are endowed with inner orientation, induce an outer orientation on the elements of the dual complex.

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The densities and the rates are said to inherit the association from their corresponding global variables. February Learn how and when to remove this template message. Please introduce links to this page from related articles ; try the Find link tool for suggestions. In turn, the time intervals connecting two adjacent dual time instants are called dual time intervals. tontu

The Mathematical Structure of Classical and Relativistic Physics : A General Classification Diagram

On the variational formulation for linear initial value problems E Tonti Annali di Matematica pura ed applicata 95 1, The fact that physical variables are associated with space and time elements endowed with inner or outer orientation and that space and time elements of a primal and a dual cell complex can be classified as shown on the right-hand side of Figs. This is not customarily considered in vector calculus or in physics.


New articles related to this author’s research. 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. The very tpnti that we create volume, surface or line densities highlights that the corresponding global variables are associated with volumes, surfaces and lines.

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: The Best Books of Description The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify fnzo for their existence.

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Email address for updates. A cell complex and its dual constitute a valid framework to describe the association of physical wnzo with the oriented space elements.

Speaking about analogies in different physical theories, Maxwell wrote in Withoutabox Submit to Film Festivals.