A treatise on gyrostatics and rotational motion . eep upright. The top sleeps more easily the greater C and the smaller a top, tapering to the peg, will spin upright at a lower angular speedon its head than upon its peg: a holt, with rounded end and massive head,will spin upright head down at a lower speed than when supported onthe end. 102 GYROSTATICS CHAP. As we have seen already, 17, II, the roots of the steady motion equation(On — ,oHd)ix= My// are imaginary if CPn2—4AMgr/tcos6 is a weak top cannot spin with its axis inclined to the upward verticalat a smaller an

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A treatise on gyrostatics and rotational motion . eep upright. The top sleeps more easily the greater C and the smaller a top, tapering to the peg, will spin upright at a lower angular speedon its head than upon its peg: a holt, with rounded end and massive head,will spin upright head down at a lower speed than when supported onthe end. 102 GYROSTATICS CHAP. As we have seen already, 17, II, the roots of the steady motion equation(On — ,oHd)ix= My// are imaginary if CPn2—4AMgr/tcos6 is a weak top cannot spin with its axis inclined to the upward verticalat a smaller angle than cos_1(C-//-/4AM;///). [Of course if the couple isnot supplied by gravity the equivalent for M;/// must be used on theseconditions. | 15. Rouths graphical representation of rise and fall of rise and fall of a top may 1- illustrated graphically as follows (Routh, , § 202). Recalling that we have o=(2E-0»2)/A, (3 = G,!A, a=2Mgh/A,b=C/A, we consider the two quantities A/i A//M//, Aa/aMh. First we notice that if the.

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