The Applications of Elliptic Functions
The Applications of Elliptic Functions
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Then, from the principles of the Conservation of Energy and Momentum, we obtain the equations (Routh, Rigid Dynamics) i A (dO/dty + \A sm 2 0(aV/cZ0 2 = Wg(c - h cos 0), ...... ( 1 ) ^sin 2 0(^/^0 + ^ cos0=^, ...................... (2) where r denotes the constant angular velocity of the top about its axis of figure OC, d\frjdt the angular velocity of the verti cal plane through Ox and OC, h the distance of the centre of gravity G from 0, W Ib. The weight of the top, and C, A its moments of ine...rtia about the axis of figure OC } and about any axis through at right angles to OC.
218 ELLIPTIC INTEGRALS IN GENERAL, Putting A/Wh = l=OP, as in the simple pendulum, then P is the centre of oscillation for plane vibrations.
The elimination of d\fsldt between equations (1) and (2) gives = (/(cos cos a)(cos cos /3)(cos d), ...... (3) suppose ; the inclination of the axis of the top to the vertical being supposed to oscillate between a and /3, a > > /3, or cos a
What to read after The Applications of Elliptic Functions?
You can find similar books in the "Read Also" column, or choose other free books by G George Greenhill to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Then, from the principles of the Conservation of Energy and Momentum, we obtain the equations (Routh, Rigid Dynamics) i A (dO/dty + \A sm 2 0(aV/cZ0 2 = Wg(c - h cos 0), ...... ( 1 ) ^sin 2 0(^/^0 + ^ cos0=^, ...................... (2) where r denotes the constant angular velocity of the top about its axis of figure OC, d\frjdt the angular velocity of the verti cal plane through Ox and OC, h the distance of the centre of gravity G from 0, W Ib. The weight of the top, and C, A its moments of ine...rtia about the axis of figure OC } and about any axis through at right angles to OC.
218 ELLIPTIC INTEGRALS IN GENERAL, Putting A/Wh = l=OP, as in the simple pendulum, then P is the centre of oscillation for plane vibrations.
The elimination of d\fsldt between equations (1) and (2) gives = (/(cos cos a)(cos cos /3)(cos d), ...... (3) suppose ; the inclination of the axis of the top to the vertical being supposed to oscillate between a and /3, a > > /3, or cos a
What to read after The Applications of Elliptic Functions?
You can find similar books in the "Read Also" column, or choose other free books by G George Greenhill to read onlineMoreLess
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