DOTATION OF A PLANET 309 



KOTATION OF A PLANET 



253. As a first example of the use of these equations, let us 

 examine the motion of a rigid body, symmetrical about an axis, 

 acted on by forces all of which pass through the center of gravity. 

 These conditions approximately represent those which obtain when 

 a planet moves in its orbit, or a star in space. 



Let us take the center of gravity as origin and the axis of sym- 

 metry as axis 1. Let the moments of inertia be A, B y B. Then the 

 equations of motion are 



' ^ = ' If < 134 > 



*^=*(S-4> V 1 , (135) 



B8 = -(U-4)y,. (136) 



The first equation gives at once that 1 is constant, say equal 

 to ft. If we write 



equations (135) and (136) become 



** , < 138 > 



-* = 



of which the solution is o> 2 =JE cos (Jet -+- e) ; 

 and equation (137) now leads at once to 



&) 3 = E sin (Jet + e). 



Thus the components of angular velocity at the instant t are 

 ft, E cos (Jet + e), E sin (Jet + e), 



