The Theory of Screws Microform a Study in the Dynamics of a Rigid Body
The Theory of Screws Microform a Study in the Dynamics of a Rigid Body
Robert S Robert Stawell Ball
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When X is found, the cylindroid (TJ X) can be drawn, and thus p is determined. The position of p on C' will point out the screw on C, about which the body will commence to twist, while the position of p on (rj, X), and the known intensity of the wrench on ?;, will determine the intensity of the wrench on X. t 2 CHAPTER XI. THE DYNAMICS OF A RIGID BODY, WHICH HAS FREEDOM OF THE THIRD ORDER. 107. Introduction. The dynamics of a rigid body which has freedom of the third order, possesses a special ...claim to attention, for, included as a particular case, we have the celebrated problem of the rotation of a rigid body about a fixed point. In the theory of screws the screw complex of the third order is characterised by the feature that the reciprocal screw complex is also of the third order, and this is a fertile source of interesting theorems. We shall first study the screw complex of the third order, and its reciprocal. We shall then show how the instantaneous screw, corresponding to a given impulsive screw, can be determined for a rigid body whose move- ments are prescribed by any screw complex of the third order.
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