CHAPTEK I. 



KINEMATICS OF A POINT. LAWS OF MOTION. 



1. Dynamics. Dynamics or Mechanics is the science of motion. 

 It is the fundamental subject of Physics, since it is the aim of 

 scientists to reduce the characterization of all physical phenomena 

 to description of states of motion. The problem of dynamics, 

 according to Kirchhoff 1 ), is to describe all motions occurring 

 in nature in an unambiguous and the simplest manner. In addition 

 it is our object to classify them and to arrange them on the 

 basis of the simplest possible laws. The success which has 

 attended the efforts of physicists, mathematicians, and astronomers 

 in achieving this object, from the time of Galileo and Newton 

 through that of Lagrange and Laplace to that of Helmholtz and 

 Kelvin, constitutes one of the greatest triumphs of the human 

 intellect. . 



2. Kinematics. That which moves is matter. The properties 

 of matter may be left for later consideration. We may, however, 

 describe motions without considering the nature of that which is 

 moved, this forms a special branch of our subject known as 

 Kinematics. 



Kinematics is merely an extension of geometry and may be called 

 geometry of motion, for while in geometry we consider the properties 

 of space, in Kinematics we consider also the idea of time, giving 

 us another variable. Since the position of a point in space is known 

 when its three rectangular Cartesian coordinates with respect to a 

 definite system of axes are given, its motion is completely described 

 if its coordinates are given for all instants of time, or are known 

 functions of the time. Analytically 



The functions f 1} f%, f z must be continuous, since in no actual motion 

 does a point considered disappear in one position to reappear after 



1) Kirchhoff, Vorlesungen fiber mathematische Physik. Mechanik, p. 1. 



1* 



