By A. I. Lurie (auth.)

This is a translation of A.I. Lurie classical Russian textbook on analytical mechanics. a part of it's in keeping with classes previously held via the writer. It deals a consummate exposition of the topic of analytical mechanics via a deep research of its so much primary ideas. The e-book has served as a table textual content for no less than generations of researchers operating in these fields the place the Soviet Union comprehensive the best technological leap forward of the XX century - a race into area. these and different similar fields remain intensively explored due to the fact that then, and the ebook basically demonstrates how the basic options of mechanics paintings within the context of updated engineering difficulties. This publication might help researchers and graduate scholars to obtain a deeper perception into analytical mechanics.

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A rigid body having a fixed point is a more general example. It is assumed here and throughout the rest of this book that the reader is acquainted with the basic principles of rigid body kinematics which can be found, for instance, in [56]. The position of this body may be prescribed by nine direction-cosines (}:ik which are cosines of the angles between rectangular axes fixed relative to the body and rectangular axes fixed in space. The constraint equations are six familiar relationships, three of which express the fact that the sum of the three squares of direction-cosines with respect to each fixed axis is equal to unity and the other three state the conditions of mutual orthogonality of the movable axes.

In addition to this, the first angle takes values from the interval [0, 7f] (or [-7f / 2, 7f / 2]) , whereas the other two vary from 0 to 27f. 54 2. 3. A well-known example of Euler's angles in astronomy uses the following set of angles: nand i determine the position of the orbital plane whilst w provides the direction for a reference axis in this plane, see Fig. 2. The first angle n is the longitude of the ascending node N of a planet and plays the role of the precession angle. The second angle i is the angle between the orbital plane and the reference fixed plane O~ry and is the nutation angle.

Table 2 takes the form II II II II x y z ~ 'Tl II 1 II I 'Ij;+ip II - ('Ij; + cp) I 1 II {) sin 'Ij; I -{)cos'lj; ( {) sin ip {) cos cp 1 Table 2* of the direction cosines II II I" II 60 2. Rigid body kinematics - basic knowledge Although angles 'IjJ and cP can take any values, the axes of the same name remain close to each other. Tables 3 and 6 differ fundamentally from the above table. The diagonal elements in these tables will differ from unity to second order only if all three angles are small.

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