An Elementary Treatise On Dynamics Containing Applications to Thermodynamics W
An Elementary Treatise On Dynamics Containing Applications to Thermodynamics W
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Dynamics Containing Applications to Thermodynamics W Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On Dynamics Containing Applications to Thermodynamics W
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To quickly assess the difficulty of the text, read a short excerpt:
#3 ^3 c 3 - 1 But it is easy to see that this condition is fulfilled, for putting tfi b x ^i a 2 b 2 Co Ch O-i c 6 = A, and denoting the former determinant by A', we have, by the multiplication of the determinants, AA' = - A', and therefore A' = 0.
Hence we conclude that if a rigid body have a fixed point, any two positions have a line in common. Again, dx = £dai + r)db x + Zdd, dy = %da 2 + r\db 2 + £dc 2, ' dz = £da 3 + rjdb 3 + %dc z ; but since, at the beginning of the motion, £, rj, £ coin...cide with x, y, z, we have at that instant a x = cos o t ; . *. Dch = - sin a x da x = 0, since a x = 0. In like manner db 2 = 0, dc 6 - ; also a x b x + a 2 b 2 + a A b 3 = 0.
Differentiating, and remembering that initially a x = 1, a 2 = 0, # 3 = 0, £>i = 0, b 2 = 1, 6 3 = 0, we have db x + da 2 = 0.
In like manner dc x + da 3 = 0, db z + dc 2 =0.
Motion of a Body having a Fixed Point. 323 Let now da 2 = dip, db^ = dO, dc y = d$ ; then dx=-i)d\p+ Z>d$ = - ydxp + zd
To quickly assess the difficulty of the text, read a short excerpt:
#3 ^3 c 3 - 1 But it is easy to see that this condition is fulfilled, for putting tfi b x ^i a 2 b 2 Co Ch O-i c 6 = A, and denoting the former determinant by A', we have, by the multiplication of the determinants, AA' = - A', and therefore A' = 0.
Hence we conclude that if a rigid body have a fixed point, any two positions have a line in common. Again, dx = £dai + r)db x + Zdd, dy = %da 2 + r\db 2 + £dc 2, ' dz = £da 3 + rjdb 3 + %dc z ; but since, at the beginning of the motion, £, rj, £ coin...cide with x, y, z, we have at that instant a x = cos o t ; . *. Dch = - sin a x da x = 0, since a x = 0. In like manner db 2 = 0, dc 6 - ; also a x b x + a 2 b 2 + a A b 3 = 0.
Differentiating, and remembering that initially a x = 1, a 2 = 0, # 3 = 0, £>i = 0, b 2 = 1, 6 3 = 0, we have db x + da 2 = 0.
In like manner dc x + da 3 = 0, db z + dc 2 =0.
Motion of a Body having a Fixed Point. 323 Let now da 2 = dip, db^ = dO, dc y = d$ ; then dx=-i)d\p+ Z>d$ = - ydxp + zd
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