This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ...is invariably attached to the given rigid system (i.e when dvr'/dt= o), that is to say, in the equation w = = Vpw., dl With a given fixed point C of the system, always tacitly assumed. Now, such vectors are for instance the three unit vectors x, x2, xj representing the rigid system's principal axes, these certainly ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ...is invariably attached to the given rigid system (i.e when dvr'/dt= o), that is to say, in the equation w = = Vpw., dl With a given fixed point C of the system, always tacitly assumed. Now, such vectors are for instance the three unit vectors x, x2, xj representing the rigid system's principal axes, these certainly being attached to the system. Hence, we can put, in the last equation, w = xj, or x2, or x3, and thus we shall obtain the three vectorial differential equations xVpxj x2 = Vpx2 J-(46) x3 = Vpx3 J which can be regarded as the expression of the kinematical relations. In this system of equations, the rdle of all the three principal axes is the same. It is true that we have here three unit vectors xl, etc., amounting to six scalars, whereas the rotating rigid system has only three degrees of freedom; in other words, Xv x2, x3 are not mutually independent variables, as 6, p, are, but, on the other hand, by using them and the form (46), none of the moving axes is specially distinguished, so that the formulae show a perfect symmetry. Remember that xj, etc., are not only unit vectors, but also mutually perpendicular; we have not only v 2--i v- 2---v" 2--T Vi vVi) Q S but also x2x3 = x3xj = xjx2 = o, that is, we have in reality only three independent scalar parameters, i.e. as many as are the degrees of freedom of the system in question. We may, however, retain xj, x2, x3 in the kinematical relations, keeping in mind the last scalar conditions, but not using them explicitly for the process of elimination. This method of treatment will secure symmetry, and thus, for general considerations, will be more convenient than scalar parameters of which the number is explicitly reduced to three. In the kinematical relations (46) the fluxes xj, etc., ...
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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