DYNAMICS OF A POINT. 



1378. A point describes a certain curve, and initially the 

 acceleration is normal ; when the direction of motion has turned 

 through an angle <, that of acceleration has turned through 



2<inthe same sense; prove that the acceleration cccos<j> , 



the velocity oc cos <, and the angular velocity of the tangent oc the 

 acceleration. 



1379. A point describes an ellipse under accelerations to the 

 foci which are one to another, at any point, inversely as the focal 

 distances of the point : find the law of either force; prove that 

 tin- velocity of the point varies as the conjugate diameter, and 

 that the periodic time is 



CD being the angular velocity about the centre at the end of either 



axis. 



1380. A parabola is described under constant acceleration; 

 that, if <, be the angles which the tangent and the direc- 

 tion of the acceleration at any point make with the directrix, 



3 tan ^ cos* = ( 



1381. A point moves with constant acceleration, which is 

 initially normal; and when tin- direction of motion has turned 

 through an angle <, that of acceleration has turned through in$ in 

 the same sense; prove that the intrinsic equation of the rune 

 described is 



Determine the curve when m= 1, 2, or 3. 



1382. A point describes a curve, whirl, lies en a cone of re- 

 volution and crosses all the generating lines at a constant angle, 



under acceleration whose direction always intersects the axis; 



