METHODS AND APPLICATIONS. 

 CHAPTER IX. 



MOTIONS OF FREE PARTICLES IN GIVEN FIELDS OF FORCE. 



160. THE application of the principles which have been laid 

 down in previous Chapters to the discussion of the motions of 

 particles in particular circumstances is the part of our subject 

 usually described as " Dynamics of a Particle." We shall devote 

 to it the two following chapters, and shall have occasion to refer to 

 it again in Chapter XII. This part of our subject divides itself 

 into two main branches, referring respectively to free motions 

 under given forces, and to constrained and resisted motions taking 

 place under forces which are not all given. We confine our 

 attention in the present Chapter to free motions. 



We have thus to consider the motion of one particle, or of 

 several particles, relative to a given frame, when each particle is 

 under the action of forces relative to the frame which are given at 

 every point. Physically such forces are presumed to arise from 

 the actions upon the particle of other particles ; but for our 

 purpose the important thing is that they produce given accelera- 

 tions, and in many cases the way in which the acceleration arises 

 need not be taken into account. Further when we are consider- 

 ing the motion of a single particle, whose acceleration is given, it 

 is immaterial what mass we attribute to the particle, and we 

 can therefore, if we wish, take its mass to be the unit of mass ; but 

 for the sake of comparison with other cases we shall generally 

 take it to have a given mass. When we are considering the 

 motions of several particles we must suppose each particle to have 

 a given mass. 



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