...be the co-ordinates of one angular point; x ìi Vìi z i the co-ordinates of another; and so on; let x, y, ~z be the co-ordinates of the centre of gravity of the pyramid: then y= i (yi (5) Toßnd the centre of gravity of any pyramid having a plane lose. Divide...

...plane of reference being that of xy, and the axis of x the line from which -fy and a are measured; let x, y, z' be the co-ordinates of the centre of gravity of the disturbing body referred to the same axes; and let a;,, y lt 2, be the co-ordinates of 8m referred...

...plane of reference being that of xy, and the axis of x the line from which -ty and a are measured ; let x, y , z be the co-ordinates of the centre of gravity of the disturbing body referred to the same axes; and let a?,, y lt 2, be the co-ordinates of Sm referred...

...3b>&-2nY=u, Zm-ZmZ=0, (4) which are the general equations for the motions of a system of bodies. 8. Let x,, y,, z,, be the coordinates of the centre of gravity of the system, and, by differentiation of the equations for the co-ordinates of the centre of gravity,...

...particle along the axes of x, y, z; then, by Art. 26, Similarly Y= /*,& + n^ + p a y 2 + and Z=fi x ~ Let x, y, z be the co-ordinates of the centre of gravity of a system of particles, whose masses are proportional to /*,, ii s , PI,... placed at the respective fixed...

...Art. 26, Similarly F= /x^ + ^ 2 y 2 + p,j/ , + ...... , and £"= /Vi + /V* + /V» + ...... x Let S, y, z be the co-ordinates of the centre of gravity of a system of particles, whose masses are proportional to /*i» /VM S. ... placed at the respective fixed...

...4. Any Solid. Let x, y, z, be the co-ordinates of any point whatever within any assigned solid; let x, y, ~z, be the co-ordinates of the centre of gravity of this solid; then \\\xdxdydz \\\ydxdydz I \\zdxdydz x 111 dxdydz 111 dxdydz \ \\dxdydz where each of...

...given direction is TO TT . Hence the resolved part of the momentum of the whole system is 2m -5- . Let (x, y, z} be the co-ordinates of the centre of gravity of the system and M the whole mass. Then MX = "Zmx ; ,.djc _ dx fl*l* Hence the resolved part of the momentum...

...centre of gravity of the base with the vertex at a point £th from the base. 22. GENERAL FORMULAE. If x, y, z be the coordinates of the centre of gravity of a system of bodies, STABLE, UNSTABLE, AND NEUTRAL EQUILIBRIUM. 23. A body is said to be in stable equilibrium...

...find their motion. The mode of using D'Alembert's Principle for the solution may be stated thus. Let x, y, z be the co-ordinates of the centre of gravity of any one of these bodies referred to three rectangular axes fixed in space. Let three other co-ordinates...