The name of C. G. J. Jacobi is familiar to every student of mathematics, thanks to the Jacobion determinant, the Hamilton-Jacobi equations in dynamics, and the Jacobi identity for vector fields. Best known for his contributions to the theory of elliptic and abelian functions, Jacobi is also known for his innovative teaching methods and for running the first research seminar in pure mathematics. A record of his lectures on Dynamics given in 1842-43 at Konigsberg, edited by A. Clebsch, has been available in the original German. This is an English translation. It is not just a historical document; the modern reader can learn much about the subject directly from one of its great masters.

Bibliographic Information

Book Title: Jacobi's Lectures on Dynamics
Book Subtitle: Delivered at the University of Konigsberg in the Winter Semester 1842-1843 and According to the Notes Prepared by C. W. Brockardt
Editors: A. Clebsch
Series Title: Texts and Readings in Mathematics
DOI: https://doi.org/10.1007/978-93-86279-62-0
Publisher: Hindustan Book Agency Gurgaon
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Hindustan Book Agency (India) 2009
eBook ISBN: 978-93-86279-62-0Published: 15 August 2009
Edition Number: 2
Number of Pages: 350
Topics: Mathematics, general

Publish with us

Policies and ethics

Jacobi's Lectures on Dynamics

Editors:

Sections

Buy it now

Other ways to access

Table of contents (36 chapters)

Front Matter

Introduction

The Differential Equations of Motion

The Principle of Conservation of Motion of the Centre of Gravity

The Principle of Conservation of ‘vis viva’

The Principle of Conservation of Surface Area

The Principle of Least Action

Further considerations on the principle of least action—The Lagrange multipliers

Hamilton’s Integral and Lagrange’s Second Form of Dynamical Equations

Hamilton’s Form of the Equations of Motion

The Principle of the Last Multiplier

Survey of those properties of determinants that are used in the theory of the last multiplier

The multiplier for systems of differential equations with an arbitrary number of variables

Functional Determinants. Their application in setting up the Partial Differential Equation for the Multiplier

The Second Form of the Equation Defining the Multiplier. The Multipliers of Step Wise Reduced Differential Equations. The Multiplier by the Use of Particular Integrals

The Multiplier for Systems of Differential Equations with Higher Differential Coefficients. Applications to a System of Mass Points Without Constraints

Examples of the Search for Multipliers. Attraction of a Point by a Fixed Centre in a Resisting Medium and in Empty Space

The Multiplier of the Equations of Motion of a System Under Constraint in the first Langrange Form

The Multiplier for the Equations of Motion of a Constrained System in Hamiltonian Form

Hamilton’s Partial Differential Equation and its Extension to the Isoperimetric Problem

About this book

Bibliographic Information

Publish with us

Buy it now

Other ways to access

Navigation

Editors:

Sections

Buy it now

Buying options

Other ways to access

Table of contents (36 chapters)

Front Matter

About this book

Bibliographic Information

Publish with us

Buy it now

Buying options

Other ways to access

Search

Navigation