Geometry of Hamilton and Lagrange Spaces

Cover of: Geometry of Hamilton and Lagrange Spaces |

Published by Kluwer in Germany .

Written in English

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Subjects:

  • Lagrange spaces.,
  • Hamilton spaces.

Edition Notes

Book details

StatementRadu Miron, Dragos Hrimiuc, Sorin V.Sabau.
SeriesFundamental theories of physics -- vol.118
ContributionsMiron, Radu.
The Physical Object
Paginationxv, 338 p. ;
Number of Pages338
ID Numbers
Open LibraryOL22113293M
ISBN 101402003528

Download Geometry of Hamilton and Lagrange Spaces

The title of this book is no surprise for people working in the field of Analytical Mechanics. However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two.

Get this from a library. The geometry of Hamilton and Lagrange spaces. [Radu Miron;] -- "This monograph presents for the first time the foundations of Hamilton Geometry. The concept of Hamilton Space, introduced by the first author and investigated by the authors, opens a new domain in.

The title of this book is no surprise for people working in the field of Analytical Mechanics. However, the geometric concepts of Lagrange space and Hamilton space are completely new.

The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and.

However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A.

However, the geometric concepts of Lagrange space and Hamilton space are completely new. The geometry of Lagrange spaces, introduced and studied in [76],[96], was ext- sively examined in the last two decades by geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and by: Request PDF | On Jan 1,R Miron and others published The Geometry of Hamilton and Lagrange Spaces | Find, read and cite all the research you need on ResearchGate.

The Paperback of the Complex Spaces in Finsler, Lagrange and Hamilton Geometries by Gheorghe Munteanu at Barnes & Noble. FREE Shipping on Author: Gheorghe Munteanu. This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics.

It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, ). It contains the general theory Geometry of Hamilton and Lagrange Spaces book higher order Hamilton spaces H (k)n, k>=1, semisprays, the canonical nonlinear connection,Author: R.

Miron. The book consists of thirteen chapters. The first three chapters present the topics of the tangent bundle geometry, Finsler and Lagrange spaces.

Chapters are devoted to the construction of geometry of Hamilton spaces and the duality between these spaces and Lagrange spaces. The dual of a Finsler space is a Cartan space.

Skip to main content. LOGIN ; GET LIBRARY CARD ; GET EMAIL UPDATES ; SEARCH ; Home ; About Us. Those who downloaded this book also downloaded the following books. X The Geometry of Hamilton & Lagrange Spaces ge geometry, discussed in Chapter 3, the metric tensor is obtained by taking the Hessian with respect to the tangential coordinates of a smooth function L defined on the tangent bundle.

This function is called a regular Lagrangian provided the Hessian is nondegenerate, and no other conditions are. In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces.

Finsler geometry had a period of incubation long enough, so that few math­ ematicians (E. Cartan, L. Berwald, S.S Brand: Springer Netherlands.

Title: Book Review: The Geometry of Hamilton and Lagrange Spaces. By Radu Miron, Dragos Hrimiuc, Hideo Shimada, and Sorin V. Sabau. p., Kluwer Academic Publishers.

Complex Spaces in Finsler, Lagrange and Hamilton Geometries | From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of P. Finsler from (Fi]).

In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self. The book is divided in three parts: I.

Lagrange and Hamilton spaces; II. Lagrange and Hamilton spaces of higher order; III. Analy-tical Mechanics of Lagrangian and Hamiltonian mechanical systems. The part I starts with the geometry of tangent bundle (TM,π,M) of a File Size: 1MB. Book Review: The Geometry of Hamilton and Lagrange Radu Miron, Dragos Hrimiuc, Hideo Shimada, and Sorin V.

Sabau. p., Kluwer Academic Publishers Author: Solange F. Rutz. The concept of Finslerian and Lagrangian structures were introduced in the papers [9,13] and the theory of higher order Lagrange and Hamilton spaces were discussed in [10, 11,12]. Further, the Author: Radu Miron. The geometry of Lagrange and Hamilton spaces is the geometrical theory of these two sequences.

The applications in Mechanics, Relativity, Relativistic Optics, Varia-tional Calculus, Optimal Control or Biology use the previous sequences. There is a natural extension of this geometry given to the higher-order Lagrange and Hamilton geometry. The Hamiltonian geometry is geometrical study of the sequence II.

The part II of the book is devoted to the notions of Lagrange and Hamilton spaces of higher order. The geometrical theory of the total space of k--tangent bundle [k] M, k [greater than or equal to] 1, is studied generalizing, step by step the theory from case k = 1.

There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M.

Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. Szilasi (Spray and Finsler Geometry).5/5(1).

The Geometry of Hamilton and Lagrange Spaces by Radu Miron Al. Cuza University, lafi, Romania Drago$ Hrimiuc University of Alberta, Edmonton, Canada Hideo Shimada Hokkaido Tokai University, Sapporo, Japan and Sorin V. Sabau Tokyo Metropolitan University, Tokyo, Japan KLUWER ACADEMIC PUBLISHERS N E W YORK, BOSTON, DORDRECHT, LONDON, MOSCOW.

adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A. Link back to: arXiv, form interface, contact. Browse v released Feedback?. If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact [email protected] for [email protected] for Cited by: In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces.

Finsler geometry had a period of incubation long enough, so that few math- ematicians (E. Cartan, L. Berwald, S.S. Chem Brand: Gheorghe Munteanu. Finsler and Lagrange Geometries by Mihai Anastasiei,available at Book Depository with free delivery worldwide.

Minkowski geometry is a non-Euclidean geometry in a finite number of dimensions that is different from elliptic and hyperbolic geometry (and from the Minkowskian geometry of spacetime). Here the linear structure is the same as the Euclidean one but distance is not "uniform" in all directions.

Instead of the usual sphere in Euclidean space, the unit ball is a general symmetric convex set. The Geometry of Hamilton and Lagrange Spaces (Fundamental Theories of Physics) by R.

Miron, Dragos Hrimiuc, Hideo Shimada, Sorin V. Sabau 1 edition - first published in The geometry of Hamilton and Lagrange spaces, Kluwer Academic Publishers, FTPH no., ISBN MR (e) I. Bucataru, R. Miron, Finsler-Lagrange Geometry.

Applications to dynamical systems, Ed. Complex Spaces in Finsler, Lagrange and Hamilton Geometries From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of.

The Geometry of Hamilton and Lagrange Spaces Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Space is the boundless three-dimensional extent in which objects and events have relative position and direction.

Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as concept of space is considered to be of fundamental importance to an understanding.

Antonelli and T. Zastawniak (eds.), Lagrange Geometry, Finsler Spaces and Noise Applied in Biology and Physics, Pergamon Press, Mathematical and Computer Modelling, 20 () no. 4/5. Antonelli and R.

Miron eds., Lagrange and Finsler Geometry Applications to Physics and. William Rowan Hamilton ( – ) was an Irish mathematician and child prodigy.

Joseph-Louis Lagrange was a Greek mathematician and is often called the father of geometry. He published a book Elements that first introduced Euclidean geometry and contained many important proofs in geometry and number theory.

It was the main. Section 1. Lagrange and Hamilton Geometry and Applications in Control.- Curvature tensors on complex Lagrange spaces.- Symplectic structures and Lagrange geometry.- A geometrical foundation for Seismic ray theory based on modern Finsler geometry Jump to Content Jump to Main Navigation.

Home About us Subject Areas Contacts About us Subject Areas Contacts. The Euler{Lagrange equation is a necessary condition: if such a u= u(x) exists that extremizes J, then usatis es the Euler{Lagrange equation.

Such a uis known as a stationary function of the functional J. Note that the extremal solution uis independent of the coordinate system you choose to represent it (see Arnold [3, Page 59]). For File Size: KB. Symplectic geometry can also be applied in curved spaces or manifolds.

We consider a surface to be the integral of infinitesimal parallelograms and define oriented areas by integrating the shadows or projections of these elements.

Phase Fluid. Hamiltonian mechanics is essentially the symplectic geometry of phase space. This book provides a comprehensive introduction to modern global variational theory on fibred spaces.

It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and.

They are studied directly and as 'dual' geometry, via Legendre t: latex2e, pages, monograph published by Kluwer in Topics: Mathematics - Differential Geometry, Mathematical PhysicsAuthor: Radu Miron.

In fact, half of the book "Lagrange Geometry, Finsler Spaces and Noise Applied in Biology and Physics", published in the collection "Mathematical and Computer Modelling" () at Pergamon Pres-USA, is edited by Radu Miron and his fellow workers siei, iu, c and A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D -dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects in the everyday example, the volume of a rectangular box is found by measuring its length.The book contains a collection of works on Riemann–Cartan and metric-affine manifolds provided with nonlinear connection structure and on generalized Finsler–Lagrange and Cartan–Hamilton geometries and Clifford structures modelled on such manifolds.

The authors develop and use the method of anholonomic frames with associated nonlinear.

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