tailieunhanh - A form of equation of motion of a mechanical system

The one of important problems of dynamics of a niultibody system its to establish automatically the equations of motion. In the present work it is constructed a form of equations of motion, which is useful for programming the problem of a multibody system, especially for applying the symbolic method in the automatical establishment of equations of motion of a multibody system. | T\'p chi Ca h9c Journal of , NCNST of Vietnam T. XVII, 1995, No 3 (45 - 48) A FORM OF EQUATION OF MOTION OF A MECHANICAL SYSTEM DO SANH Hanoi Technology University The one of important problems of dynamics of a niultibody system is .to establish automatically the equations of motion. In the present work it is constructed a form 'of equations of motion, which is useful for programming th,e problem of a multibody system, especially for applying the symbolic method in the automatical establishment of equations of motion of a multibody system. §1. A FORM OF EQUATIONS OF MOTION OF A MECHANICAL SYSTEM Let us consider a holonomic mechanical system of n degrees of freedom. Denote the generalized coordinates of the considered system by q; (i = 1, n). Suppose that the considered system has the matrix of inertia A_, which is an n X n positive define symmetric matrix. The elements of this· matrix depend on the generalized coordinates, . () where q is an n X 1 column matrix, which has the elements to be the generalized coordinates. The expres;j_on of the kinetic energy can be written in the foi-m: ·_·q A . T = -q 2- where q is () - the n X 1 column matrix of generalized velocities; fuj,~. qT is the transpose of the matrix of () Denote the generalized forces of applied forces by Q;(t, q;, q;) matrix: (i = 1, n) and Q is the column () To write the equations of motion we can use the equations of Lagrange of second kind: () From these equations we have found the form of equations of motion, that is, A·§+ci'·D·ra ra mi/t d~ng phlrong trlnh chuyEn dqng thkh h9'P cho vi~c thil!t I~p tv dqng cOic ph>rong trlnh chuy~n dqng cda m9t h~ co hgc n6i chung va co h~ nhi~u v~t n6i rieng tren may tinh ca nhan. D~ vil!t ph1rong trlnh chuyrong trlnh neu tren d>rg-c stlc dv:ng rO:t c6 hi~u qua khi sd- dv:ng cac phh m~m nh>r Ch1r0ng trlnh Maple, Ch>rong trlnh Maxima d~ thigt l~p phlrong trlnh chuy~n dc?ng cda co h~ mgt chl trv:·c tie'p blng cac