A Treatise On Gyrostatics And Rotational Motion
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Determination of azimuthal displacement for periodic motion of weak top. To find ^p we have, since fi = hn, \L=hn^ r, = rr-r- W ^ 1—z^ 1+2 1 1 1 I _ 1 ___^'__j-__!^ ^- (2V ^"^ iT:-^rT^^rT".~r+7^"n^ (i+u^'^(i+^-)^^+^ ' 118 GYROSTATICS CHAP.
This expression may be carried as far as may be desired by substitution for 1/(1+2) on the right of the expression on the right, and so on. It is sufficient at present to use the first two terms on the right of (2). Thus we get ^= *!i-(l _^) = ^(l_^sin,..); (...3) and therefore iI/=- t-^—7^ — — zu' cos mt ! +i/'n (4) The time t is here reckoned from the instant at which the axis is at the mean circle z^. Hence, at t = 0, we have ^=^^^0+^^+^" (^> After half a period, that is ir/nij the axis is again at the mean circle, and ^=™iT^(-rTi)+^» (*5> In this interval the axis has risen to the vertical and fallen again to the circle Zrn- After another half period, during which the axis falls to the limiting circle and rises again to the circle z^, the value of ^p■ is given by , bn 1 f^ u' \ , ^=» n:^(2-+rT^)+V'o (7) The orthographic projection of the path on a horizontal plane is therefore a " rosette," like that indicated in Fig.
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To quickly assess the difficulty of the text, read a short excerpt:
Determination of azimuthal displacement for periodic motion of weak top. To find ^p we have, since fi = hn, \L=hn^ r, = rr-r- W ^ 1—z^ 1+2 1 1 1 I _ 1 ___^'__j-__!^ ^- (2V ^"^ iT:-^rT^^rT".~r+7^"n^ (i+u^'^(i+^-)^^+^ ' 118 GYROSTATICS CHAP.
This expression may be carried as far as may be desired by substitution for 1/(1+2) on the right of the expression on the right, and so on. It is sufficient at present to use the first two terms on the right of (2). Thus we get ^= *!i-(l _^) = ^(l_^sin,..); (...3) and therefore iI/=- t-^—7^ — — zu' cos mt ! +i/'n (4) The time t is here reckoned from the instant at which the axis is at the mean circle z^. Hence, at t = 0, we have ^=^^^0+^^+^" (^> After half a period, that is ir/nij the axis is again at the mean circle, and ^=™iT^(-rTi)+^» (*5> In this interval the axis has risen to the vertical and fallen again to the circle Zrn- After another half period, during which the axis falls to the limiting circle and rises again to the circle z^, the value of ^p■ is given by , bn 1 f^ u' \ , ^=» n:^(2-+rT^)+V'o (7) The orthographic projection of the path on a horizontal plane is therefore a " rosette," like that indicated in Fig.
What to read after A Treatise On Gyrostatics And Rotational Motion?
You can find similar books in the "Read Also" column, or choose other free books by Gray, Andrew, 1847-1925 to read onlineMoreLess
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