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action angle angular arbitrary assumed axes axis becomes body branch centre circle coefficient columns common condition cone conic consequently consider constant contains coordinates corresponding cubic curve cusps denote determine differential direction double dt dt elements ellipsoid envelope equal equation evolute expression fixed force formulæ four function give given Hence integral intersection letters manner meet multiplicity normal obtain original pairs parallel curve pass perpendicular plane points of contact pole positive principal putting quadric quantities radius reciprocal reference regard relation represent respectively result rows signs solution square substituting suppose surface tangent theorem third touch triads variable writing written zero
Side 187 - On the small oscillations of a Rigid Body about a Fixed Point under the action of any Forces, and more particularly when gravity is the only force acting," Transactions of the Boyal Irish Academy, vol.
Side 188 - ... to these directions are at right angles. III. A Free Rigid Body. 4. A free rigid body may receive any displacement by being screwed along an axis in space, the distance it travels along the axis when turned through the unit of angle being termed the pitch of the screw.
Side 50 - Д0 be the area of the triangle formed by joining the points of contact of the...
Side 189 - ... of these axes, as about a fixed axis, and its motion is always compounded of vibrations about these axes. 15. The length of the simple pendulum isochronous with the vibration about each normal axis is proportional to the square of the ratio of the corresponding diameter in the ellipsoid of equal energy to that of the momental ellipsoid.
Side 6 - I)2 = 0 ; and by reason of this property it is very easy to find the equations of the reciprocal surfaces, or plane-equations of the quartic surfaces in question. And, in the same paper, it is noticed that the surfaces of the form in question include the reciprocals of several interesting surfaces of the orders 6, 8, 9, 10, and 12 ; viz., order 6, parabolic ring : order 8, elliptic ring : order 9, centrosurface of paraboloid : order 10, parallel surface of paraboloid ; envelope of planes through...
Side 189 - A body rotating about a fixed point has throe degrees of freedom; its motion is compounded of vibrations about three normal screws whose pitch is zero, and whose directions pass through the point. NB — The screws in this case may be conveniently called the normal axes. V.
Side 9 - General Solution and Extension of the Problem of the 15 School Girls,
Side 307 - On the summation by definite integrals of geometrical series of the second and higher orders.