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الكتب الكتب 1 - 10 من 32 في... constant. Let x,, y,, z, be the co-ordinates of the centre of gravity of a flat....
" ... constant. Let x,, y,, z, be the co-ordinates of the centre of gravity of a flat plate having its middle plane coincident with the given cross-section. Then, by reasoning similar to that of Articles 74 and 78, we find the following results for the... "
A Manual of Applied Mechanics - الصفحة 62
بواسطة William John Macquorn Rankine - 1872 - عدد الصفحات: 648
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The Mathematical Diary: Containing Collections of Original ..., المجلد 1

1825
...system will be expressed by the equation dm = To apply this equation to the motion of a solid, let x, y, z, be the co-ordinates of the centre of gravity of the solid referred to the formentioned axes, and let x, y, :' be the coordinates of dm to the same...
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The Mathematical Principles of Mechanical Philosophy: And Their Application ...

John Henry Pratt - 1836 - عدد الصفحات: 616
...not be so chosen, as to simplify these expressions. PKOP. The first three may be simplified. 413. Let x, y, z be the co-ordinates of the centre of gravity of the system : and let M be the mass of the system. Then by p. 67, we have 2 . mx = Mai, 2 . my = My,...
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The Mathematical Principles of Mechanical Philosophy and Their Application ...

John Henry Pratt - 1842 - عدد الصفحات: 620
...not be so chosen, as to simplify these expressions. PROP. The first three may be simplified. 413. Let x, y, z, be the co-ordinates of the centre of gravity of the system: and let M be the mass of the system. Then by Art. 87, Ex. 25, we have 2. mx = MX, 2. my...
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A Collection of Problems in Illustration of the Principles of Theoretical ...

William Walton - 1842 - عدد الصفحات: 451
...IV. 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 - _ fffx dx dy dz _ fffy dx dy dz __ /Г/г dx dy dz = fff dxdydz' У= ffßxdydz...
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Dynamics: Or, A Treatise on Motion; to which is Added a Short Treatise on ...

Samuel Earnshaw - 1844 - عدد الصفحات: 372
...through space in a straight line. We deduce this principle from the equations of Art. 183 marked (A). Let x, y, z be the co-ordinates of the centre of gravity of the system ; then x . 2m = 2 (mx), .-. dt'z . 2m = 2 (mdfx) by differentiation, = 0, by equations (A),...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1852
...element of the mass of a body at any point x, y, z, referred to any three coordinate axes, and let x, y, z be the coordinates of the centre of gravity of the body : then - fxdm — fydm - _ fzdm л1— - ~TJ — , У=~/-17 , z—~ "П — , Jam J Jam Jam...
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A treatise on analytical statics

Isaac Todhunter - 1853
...x — , + fjtr x — 3 + pr x -3 4 rtn SYt y '' a. 'it 4 n* ',!,, „ Similarly ' 1 ' a ' « Let a, y, z be the coordinates of the centre of gravity of a system of particles, whose masses are proportional to A*n /* s , /*2) ••• pl ace< l at the respective...
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Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - 1862 - عدد الصفحات: 294
...element of the mass of a body at any point x, y, z, referred to any three coordinate axes, and let x, y, z be the coordinates of the centre of gravity of the body : then — fxdm — fydm — fzdm x~ fdm' y = ~fdm" Z = Jdm~' the limits of integrations being...
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A Manual of Applied Mechanics

William John Macquorn Rankine - 1864 - عدد الصفحات: 648
...different cross-sections are to each other as the squares of their corresponding linear dimensions. Let t denote some definite linear dimension of a cross-section...results for the whole body : — volume weight moments • /* a-, t3- dz; yW = wafyt Adz; zW = waj z i'.dz; .(3.) co-ordinates of centre of gravity >,'<?--...
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An Elementary Treatise on Rational Mechanics

John Kerr - 1866 - عدد الصفحات: 295
...weight of an element, and (xyz) be the rectangular co-ordinates of any point of the element ; and if (x' y' z'} be the co-ordinates of the centre of gravity of the body : then , 2 .w te '. 2.HM/ . 2 .iv g x — -= - , y = -= — - , S = — = — • 5 «; 2...
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