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Jacobi's Lectures on Dynamics

Delivered at the University of Konigsberg in the Winter Semester 1842-1843 and According to the Notes Prepared by C. W. Brockardt

  • Book
  • © 2009

Overview

Editors:
  1. A. Clebsch
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Part of the book series: Texts and Readings in Mathematics (TRM)

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Table of contents (36 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • A. Clebsch
    Pages 1-6

  3. The Differential Equations of Motion

    • A. Clebsch
    Pages 7-15

  4. The Principle of Conservation of Motion of the Centre of Gravity

    • A. Clebsch
    Pages 16-19

  5. The Principle of Conservation of ‘vis viva’

    • A. Clebsch
    Pages 20-32

  6. The Principle of Conservation of Surface Area

    • A. Clebsch
    Pages 33-45

  7. The Principle of Least Action

    • A. Clebsch
    Pages 46-54

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

    • A. Clebsch
    Pages 55-61

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

    • A. Clebsch
    Pages 62-71

  10. Hamilton’s Form of the Equations of Motion

    • A. Clebsch
    Pages 72-76

  11. The Principle of the Last Multiplier

    • A. Clebsch
    Pages 77-91

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

    • A. Clebsch
    Pages 92-97

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

    • A. Clebsch
    Pages 98-108

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

    • A. Clebsch
    Pages 109-115

  15. 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

    • A. Clebsch
    Pages 116-128

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

    • A. Clebsch
    Pages 129-136

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

    • A. Clebsch
    Pages 137-143

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

    • A. Clebsch
    Pages 144-153

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

    • A. Clebsch
    Pages 154-156

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

    • A. Clebsch
    Pages 157-170
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About this book

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.

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