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Jacobi’s Lectures on Dynamics

Part of the Texts and Readings in Mathematics Book Series

Editors: Clebsch, A.

DOI: 10.1007/978-93-86279-62-0

ISBN: 978-81-85931-91-3

Publisher: Hindustan Book Agency - Springer Journals

May 24, 2017

1 - 10 of 36 Chapters

LitStream

Chapter 1Introduction

Clebsch, A.

Pages: 1 –6

[These lectures will be concerned with the advantages which, for integrating the differential equations of motion, one can derive from the special form of the equations. In ‘Mécanique analytique’ one finds everything related to the problems of setting up and transforming the differential...
LitStream

Chapter 2The Differential Equations of Motion

Clebsch, A.

Pages: 7 –15

[To begin with we shall consider a free1 system of mass points. We call it a system because we assume that the points are subject to external forces not independently of one another, in which case one could consider each point by itself, but as they act mutually on one another one cannot consider...
LitStream

Chapter 3The Principle of Conservation of Motion of the Centre of Gravity

Clebsch, A.

Pages: 16 –19

[We shall now proceed to the proofs of the general principles which hold for the mechanical problems considered so far. The first of these is (cf. Lecture 1) the principle of conservation of motion of the centre of gravity.]
LitStream

Chapter 4The Principle of Conservation of ‘vis viva’

Clebsch, A.

Pages: 20 –32

[A hypothesis on the variations that under all circumstances is consistent with the equations of constraint is that one sets for each value of i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
LitStream

Chapter 5The Principle of Conservation of Surface Area

Clebsch, A.

Pages: 33 –45

[We had made the assumption that the force function U and the equations of constraint remain unchanged if one changes all the x-coordinates through one and the same constant, likewise all the y-coordinates through a second and all the z-coordinates through a third, and obtained the principle of...
LitStream

Chapter 6The Principle of Least Action

Clebsch, A.

Pages: 46 –54

[We come now to a new principle which does not give an integral, as the earlier ones did. This is the principe de la moindre action, wrongly called the principle of least action. Its importance lies, first, in the form in which it represents the differential equations of motion and secondly in...
LitStream

Chapter 7Further considerations on the principle of least action—The Lagrange multipliers

Clebsch, A.

Pages: 55 –61

[Apart from the drawback of the usual way of expressing the principle of least action in that one does not introduce the theorem of vis viva in the integral, there comes another. This one is that one says that the integral shall be the largest or the smallest, instead of saying that its first...
LitStream

Chapter 8Hamilton’s Integral and Lagrange’s Second Form of Dynamical Equations

Clebsch, A.

Pages: 62 –71

[One can substitute another principle in place of the principle of least action where also the first variation of an integral vanishes, and from which one can derive the differential equations of motion in a still simpler way than from the principle of least action. It appears that this principle...
LitStream

Chapter 9Hamilton’s Form of the Equations of Motion

Clebsch, A.

Pages: 72 –76

[After the publication of the first edition of Mécanique analytique, the most important step forward in the transformation of the differential equation of motion was made by Poisson in a paper which deals with the method of variation of constants and which appears in Volume 15 of the...
LitStream

Chapter 10The Principle of the Last Multiplier

Clebsch, A.

Pages: 77 –91

[The principle of the last multiplier accomplishes, in all cases where the integration of a system of differential equations of motion is reduced to a first order differential equation of two variables, the integration of this last equation by giving its multipliers. Here it is assumed that the...

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