1 68 DYNAMICS OF A RIGID BODY. 



Multiplying the first of these equations by Xi, the second 

 by X 2 , &c., adding the six equations thus produced, and 

 remembering that 6 and X are reciprocal, we deduce 



2 = o. 



This equation determines X" the intensity of the im- 

 pulsive reaction of the constraints. The co-ordinates of 

 the required screw 9 are, therefore, proportional to the 

 six quantities 



rjiSXi 2 - Xi2?hXi. c 



' - - ' &c - 



A 



156. Principal Screws of Inertia. We are now ena- 

 bled to determine the co-ordinates of the five principal 

 screws of inertia ; for if be a principal screw of inertia, 

 then 



whence 



with similar values for ? 2 , &c., 6 . Substituting these 

 values in the equation 



and making = x y we have- for x the equation 



p\- x pi- x pi- x pi - x ps - x ps-x 



This equation is of the fifth d egree, corresponding to 

 the five principal screws of inertia. If x' denote one of 

 the roots of the equation, then the corresponding prin- 

 cipal screw of inertia has co-ordinates proportional to 



AI Aj A 3 A 4 AS A 



