By W. O. Schiehlen (eds.)

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O. Schiehlen RIGID BODY Fig. I. Multibody system The position of a system of tial frame xi' yi' z1 Yl X1 Zl: of the center of mass bodies is given relative to an iner- by the 3xl-translation vector r. = (r . r . ] T , 1 p i .. I (I )p , (I) C. and the 3x3-rotation tensor. 1 s 1... ) , 1 1 1 1 i = I ( l)p , (2) written down for each body, Fig. 2. The translation vector rotation tensor fixed frame S. 1 characterize each body xi' yi' zi • The rotation tensor generalized coordinates ai' ei' yi K. 1 and the by a corresponding body- 1 Si depends on the three and follows from the direction cosine matrix relating the inertial frame to each body-fixed frame.

C. -1 a. T -:1. o c. -:1. v. (57) -:1. f. =F. v. -:1. -1 -:1. >... -111 -:1. The boundary conditions may allow n - l nodal deformations, called the nodal degrees of freedom. They are described by coordinates qv , v == 1, •.. , n i=l, ... ) -:1. n generalized . :1 = [ q , , . . , qn v= -g T IT T T v , .... , v ] - 1 -s (58) K. • , s v. The connection between matrices I and I. --'1 -J. -g is given by incidence an v -g , respectively, where the boundary and tran- sition conditions are regarded, I.

Erical solution of the equations. puterized derivation of equations of motion is presented in the author's lecture "Complex Nonlinear Vehicles". REFERENCES I. O. , Co•puterized Derivation of Equations of Motion, in: pynamias of MULtibody Systems, Ed. K. Magnus, Springer-Verlag, Berlin-Heidelberg-New York, 1978, 290-305. 2. Jay Tracks, Ed. by A. Slibar and H. Springer, Swets & Zeitlinger, Amsterdam, 1978, 40-48. 3. , Gyrodynamias, CISM Courses and Lectures No. 53, SpringerVerlag, Wien-New York, 1974.

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