# A Treatise on the Dynamics of a System of Rigid Bodies

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 edition. Excerpt: ...phase and sometimes the argument. The coefficient is called the frequency. It frequently happens that the real exponentials are absent from the expression for the force. This case will therefore be more particularly considered in what follows. When we wish to call attention to the absence of the real exponential, the disturbing force is often called a permanent force. When the real exponential is present with a negative index, we may call the force evanescent. Sometimes instead of the force being given, some point of the system is compelled to oscillate in a given manner. We then have some given relation between the coordinates of the system of the form ax + by + cz + &c. = Gevt sin (vt + 7) where a, b, c &c, G, g &c. are given constants. There may also be several similar relations between some or all the coordinates. In such a case we suppose these given relations to be included amongst the differential equations, though they cannot be derived from a Lagrangian function as in Art. 111. The method of finding the corresponding forced vibration given in Art. 326, will then still be applicable. 324. The general equations of motion of the second order are given in Art. 310, but in dynamics the terms which depend on the functions D and F are in general absent. The mode in which these are formed when the resisting forces are absent is explained in Art. 111. Including these resistances we may suppose that the equations of motion take the forms (An& + Ba8 + Cn)x+(A1.2& + B1.!8 + C1Ay+...=Pe-'tsm(t + a) V +ia8 ) AaB-+ BUS + C y + (Aa8 + BB+C)y +...= Qe-' sin(+/3) &c. = &c, where we have written on the right-hand side only one disturbing force in each equation as a specimen. For the sake of brevity, it will be...