Jacobi’s Lectures on Dynamics

Chapter 1 Introduction

Chapter 2 The Differential Equations of Motion

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

Chapter 4 The Principle of Conservation of ‘vis viva’

Chapter 5 The Principle of Conservation of Surface Area

Chapter 6 The Principle of Least Action

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

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

Chapter 9 Hamilton’s Form of the Equations of Motion

Chapter 10 The Principle of the Last Multiplier

Chapter 11 Survey of those properties of determinants that are used in the theory of the last multiplier

Chapter 12 The multiplier for systems of differential equations with an arbitrary number of variables

Chapter 13 Functional Determinants. Their application in setting up the Partial Differential Equation for the Multiplier

Chapter 14 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

Chapter 15 The Multiplier for Systems of Differential Equations with Higher Differential Coefficients. Applications to a System of Mass Points Without Constraints

Chapter 16 Examples of the Search for Multipliers. Attraction of a Point by a Fixed Centre in a Resisting Medium and in Empty Space

Chapter 17 The Multiplier of the Equations of Motion of a System Under Constraint in the first Langrange Form

Chapter 18 The Multiplier for the Equations of Motion of a Constrained System in Hamiltonian Form

Chapter 19 Hamilton ’s Partial Differential Equation and its Extension to the Isoperimetric Problem

Chapter 20 Proof that the integral equations derived from a complete solution of Hamilton ’s partial differential equation actually satisfy the system of ordinary differential equations. Hamilton ’s equation for free motion

Chapter 21 Investigation of the case in which t does not occur explicitly

Chapter 22 Lagrange ’s method of integration of first order partial differential equations in two independent variables. Application to problems of mechanics which depend only on two defining parameters. The free motion of a point on a plane and the shortest line on a surface

Chapter 23 The reduction of the partial differential equation for those problems in which the principle of conservation of centre of gravity holds

Chapter 24 Motion of a planet around the sun - Solution in polar coordinates

Chapter 25 Solution of the same problem by introducing the distances of the planet from two fixed points

Chapter 26 Elliptic Coordinates

Chapter 27 Geometric significance of elliptic coordinates on the plane and in space. Quadrature of the surface of an ellipsoid. Rectification of its lines of curvature

Chapter 28 The shortest line on the tri-axial ellipsoid. The problem of map projection

Chapter 29 Attraction of a point by two fixed centres

Chapter 30 Abel’s Theorem

Chapter 31 General investigations of the partial differential equations of the first order. Different forms of the integrability conditions

Chapter 32 Direct proof of the most general form of the integrability condition. Introduction of the function H , which set equal to an arbitrary constant determines the p as functions of the q

Chapter 33 On the simultaneous solutions of two linear partial differential equations

Chapter 34 Application of the preceding investigation to the integration of partial differential equations of the first order, and in particular, to the case of mechanics. The theorem on the third integral derived from two given integrals of differential equations of dynamics

Chapter 35 The two classes of integrals which one obtains according to Hamilton ’s method for problems of mechanics. Determination of the value of ( φ , Ψ ) for them

Chapter 36 Perturbation theory