INTRODUCTION

CHAPTERⅠ TRAJECTORIES IN AN ARBITRARY FIELD OF FORCE

1-8．Trajectories in the plane

9．Actual and virtualt rajectories

10-15．Trajectories in space

16-25．The inverse problem of dynamics:a method of geometric exploration

26-27．Tests for a conservative field

CHAPTER Ⅱ NATURAL FAMILIES:THE GEOMETRY OF CONSERVATIVE FIELDS OF FORCE

28．Origin and application of the natural type

29-31．Characteristic properties A and B

32．General velocity systems

33．Reciprocal systems

34．Character of the transformation T

35-44．The converse of Thomson and Tait＇s theorem

45-53．Wave propagation in an isotropic medium:properties of wave sets

54-61．A second converse problem connected with the Thomson-Tait theorem

62-67．Geometric formulation of some curious optical properties

68-72．The so-called general problem of dynamics

CHAPTER Ⅲ TRANSFORMATION THEORIES IN DYNAMICS

73-81．Projective transformations

82-91．Conformal transformations

92-94．Contact transformations

95-97．A group of space-time transformations

CHAPTER Ⅳ CONSTRAINED MOTIONS IN A FIELD．GENERALIZATION OF THE TRAJECTORY PROBLEM INCLUDING BRACHISTOCHRONES AND CATENARIES

98-114．Systems Sk defined by P=kN

115-116．Curves of constant pressure

117-118．Tautochrones

119．Non-uniform catenaries

CHAPTERⅤ MORE COMPLICATED TYPES OF FORCE

120-122．Motion in a resisting medium

123-126．Particle on a surface

127-130．The general field in space of n dimensions

131-132．Interacting particles in the plane and in space

133-141．Forces depending on the time．Trajectories and space-time curves