By Henry William Watson
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Additional resources for A Treatise on the Application of Generalised Coordinates to the Kinetics o
Any impulses applied at right angles to the tangent would generate in the extremity of the string an infinite velocity, without instantaneously affecting any other portions of the gential, since string. mass of an element ds of the string at P. the vector velo Let p P be the vector from the origin to P, Let fx da be the f>p city of P. Also let pq, pq be the corresponding vectors for a neighbouring 40 EXAMPLES OF point Q of the string. (PP is, PQ) (pp - p Q = 0. ^ =0 Thatis, or, Then, by the condition of inextensibility, constant; that or [24.
Always In this case there are three degrees of freedom, and therefore three independent velocities in terms of which the whole motion may be determined. Let these be chosen as the two components of the velocity of any point in the axis of figure, and the angular velocity about 47 INCOMPRESSIBLE FLUID. ] an axis through the same point perpendicular to the plane in which that axis moves. It is assumed that the body has no rotation about its axis of figure. If u and q be the resolved parts of the velocity of the point along and perpendicular to the axis of figure, and w the angular velocity about the axis through this point, it is clear from our general proposition that the whole kinetic energy of the body and fluid is For the reversal of the sign of u cannot A, B, C, D affect T.
Q can be expressed in the form of a determinant. The following is taken from Routh To deduce Euler s equations s Rigid Dynamics. a rigid body from Lagrange s for equations of motion. We have shewn above that components of momentum if pe , p$, p^ denote the respectively, = = Pt pe B co 2 cos ^ + A coj -f Cco 3 generalised corresponding to the coordinates 0, $, sin </>, , sin $ ^1 w x cos sin ^. </>) -fy 24 EXAMPLES OF LAGRANGE EQUATIONS. S [13. o> 2 d(f) 2 d(f> sin + ^(DJ cos(/> A o^ $ sin</>) cos </>) 0, ____.
A Treatise on the Application of Generalised Coordinates to the Kinetics o by Henry William Watson
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