The Geometry of Hamilton and Lagrange Spaces by Radu, Dragos Hrimiuc, Kideo Shimada and Sorin V. Sabau

By Radu, Dragos Hrimiuc, Kideo Shimada and Sorin V. Sabau Miron

The identify of this ebook is not surprising for individuals operating within the box of Analytical Mechanics. notwithstanding, the geometric suggestions of Lagrange house and Hamilton area are thoroughly new. The geometry of Lagrange areas, brought and studied in [76],[96], was once ext- sively tested within the final 20 years by way of geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many overseas meetings have been dedicated to debate this topic, lawsuits and monographs have been released [10], [18], [112], [113],... a wide quarter of applicability of this geometry is advised via the connections to Biology, Mechanics, and Physics and likewise through its normal surroundings as a generalization of Finsler and Riemannian geometries. the concept that of Hamilton area, brought in [105], [101] was once intensively studied in [63], [66], [97],... and it's been profitable, as a geometrical idea of the Ham- tonian functionality the basic entity in Mechanics and Physics. The classical Legendre’s duality makes attainable a ordinary connection among Lagrange and - miltonspaces. It finds new suggestions and geometrical gadgets of Hamilton areas which are twin to these that are comparable in Lagrange areas. Following this duality Cartan areas brought and studied in [98], [99],..., are, approximately talking, the Legendre duals of convinced Finsler areas [98], [66], [67]. The above arguments make this monograph a continuation of [106], [113], emphasizing the Hamilton geometry.

Show description

Read or Download The Geometry of Hamilton and Lagrange Spaces PDF

Best geometry books

Geometry for the Classroom

Meant to be used in collage classes for potential or in-service secondary tuition lecturers of geometry. Designed to provide academics wide instruction within the content material of effortless geometry in addition to heavily comparable subject matters of a marginally extra complex nature. The presentation and the modular layout are designed to include a versatile technique for the educating of geometry, one who should be tailored to assorted lecture room settings.

Basic noncommutative geometry

"Basic Noncommutative Geometry offers an advent to noncommutative geometry and a few of its purposes. The ebook can be utilized both as a textbook for a graduate path at the topic or for self-study. it is going to be helpful for graduate scholars and researchers in arithmetic and theoretical physics and all those people who are attracted to gaining an knowing of the topic.

Advances in Architectural Geometry 2014

This ebook includes 24 technical papers offered on the fourth version of the Advances in Architectural Geometry convention, AAG 2014, held in London, England, September 2014. It deals engineers, mathematicians, designers, and contractors perception into the effective layout, research, and manufacture of complicated shapes, with a purpose to aid open up new horizons for structure.

Extra resources for The Geometry of Hamilton and Lagrange Spaces

Example text

2. 7) is just the classical law of transformation of the local coefficients of a tensor field on the base manifold M. 6)). 3. 13) are d-tensor fields of type (1,2). 7 J/'-T-T dy1 is a d-vector field. N—linear connections Let N be an a priori given nonlinear connection on the manifold E = TM. 1. e. a Kozul connection or covariant derivative) on the manifold E = TM is called an N–linear connection if: 1° D preserves by parallelism the horizontal distribution N. 2° The tangent structure J is absolute parallel with respect to D, that is DJ = 0.

For any function / € F{E). 9) D l , = y% d*,- = y% are called the h- and v-deflection tensor fields of the N-linear connection D. 3. 9)' D'j = ysUsj - tfj, tfj = 5} + y*Clsj. 9)'. The d-tensor of deflections are important in the geometry of tangent bundle. 1. The geometry of tangent bundle 23 A N-linear connection D is called of Cartan type if its tensor of deflection have the property: Dl3 = 0, dtj = S'j. 10) = 0. We will see that the canonical metrical connection in a Finsler space is of Cartan type.

1) £(c) =/>(*,§),«. ,: Remark. Starting from the property that L(x,y) = F2(x,y) is energy function of the regular Lagrangian F2, we will prove in the next chapter the following two properties. Theorem A. Along with the integral curves of the Euler-Lagrange Q equations ffr' Et (F2) = 0, y* = — we have: at dt Theorem B. 2. 1. 1) can be expressed in the form where Gl is given by (4-4) 2 Proof. 3). 4) give the integral curve of the spray The vector field S is called canonical spray of the space. 2.

Download PDF sample

Rated 4.61 of 5 – based on 39 votes