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acted amplitude angles applied axes axis belonging centre co-ordinates co-reciprocal coefficient common completely condition conic conjugate constant constraints construction contains corresponding course cylindroid defined denote determined diameter direction displacement double Draw drawn Dyname equal equations expression five forces four freedom function geometrical give given Hence homographic impulsive screw impulsive wrench infinite instantaneous screw intensity intersect intervene known linear mass-chain move objects obtain pair parallel pass perpendicular pitch plane position possible present principal screws problem proportional proved quadric quantities range ratio reciprocal relation remain represented respectively result rigid body rotation satisfy screw system screw-chain screws of inertia screws of reference shown single space straight line suppose surface theorem theory third three-system twist velocity values vector whence zero zero pitch
Seite 7 - We have next to define the use to be made of the word twist. A body is said to receive a twist about a screw when it is rotated uniformly about the screw, while it is...
Seite 195 - ... ellipsoid and the cylinder. These three lines are the three harmonic axes. As to that vertical axis which appears to be one of the harmonic axes, the time of vibration about it would be infinite. The three harmonic screws which are usually found in the small oscillations of a body with freedom of the third order are therefore reduced in the present case to two, and we have the following theorem : — A rigid body which, is free to rotate about a fixed point is at rest under the action of gravity....
Seite 5 - Thus a force, and a couple in a plane perpendicular to the force, constitute an adequate representation of any system of forces applied to a rigid body.
Seite 520 - Treatise on the Theory of Screws (gr. 8°, 26 chapt., 544 p., 50 fig. and 3 plates; 18 sh.). Cambridge, University press, 1900. — Since the author's celebrated publication ,,The Theory of Screws: A study in the Dynamics of a Rigid Body...
Seite 532 - ... straight lines joining corresponding points of homographically divided spaces. The different equations and the consequences derived from them are obtained by vector analysis (p. 515 — 525). Transactions of the Royal Irish Academy, Vol. XXXI, part. V, 1898. (P. ZEEMAN.) R 1 C , 3 aa , 4 , 8. RS BALL. The Twelfth and concluding Memoir on the "Theory of Screws", with a Summary of the Twelve Memoirs.
Seite 523 - Rotors' of Professor Clifford to represent the position of a line in space." The Theory of Screws is considered and the nature of the cylindroid in Elliptic Space discussed. The general equations of motion referred to any moving axes are then found, and in a particular case they reduce to a form corresponding to Euler's equations. When there are no acting forces these equations are solved in terms of the thetafunctions. This paper has been already cited in §§ 412, 420.
Seite 170 - 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.
Seite 4 - Any given displacement of a rigid body can be effected by a rotation about an axis combined with a translation parallel to that axis.
Seite 28 - Also since the entire cylindroid (or at least its curved portion) is included between two parallel planes (§ 1 7), it follows that this conic must be an ellipse. We shall now prove that this ellipse is the locus of the feet of the perpendiculars let fall from 0 on the generators of the cylindroid. Draw in the plane of the ellipse any line TUV through T; then, since this line intersects two screws of equal pitch in T and U, it must be perpendicular to that generator of the cylindroid which it meets...