tailieunhanh - A criteria of ideality of mechanical constraints in principle of compatibility

In this article we will show the theoretical basis and algorithms for realizing these conditions in system dynamical solution on computers. | Journal of Mechanics, NCNST of Vietnam T. XVI, 1994, No 4 (33 - 36) ·A CRITERIA OF IDEALITY OF MECHANICAL CONSTRAINTS IN PRINCIPLE OF COMPATIBILITY DINH VAN PHONG Hana~· Technology University §1. INTRODUCTION With the aids of computers the principle of compatibility is convenient and powerful method for studying motion of mechanical system with constraints. The theoretical basis of method is described in [6]. The great advantage of this method is fact that reaction forces are not excluded from motion equations and so they could be directly computed with other dynamical quantities. But on the other hand the complexity of forms of motion equations doesn't allow its easy application in practice. So just algorithms which could be realized on computer make the method be powerful tool. Some examples of this trend were showed in [4, 5]. As showed in [4, 5, 6) a criteria of ideality of constraints is one of key- problems. With reaction forces in motion equations and the equations of constraints we h.~ve, a· under determined system of equations. So in order to determine completly the motion of system we must add the auxilary conditions. And in our case these conditions will be the ideality of constraints of the Appell-Frzeborski-Chetaev's type. In this article we will show the theoretical basis and algorithms for realizing these conditions in system dynamical solution on computers. §2. CRITERIA OF IDEALITY OF CONSTRAINTS Let's consider a mechanical system with n holonomic coordinates The constraints of these coordinates could be written in the matrix form: ll ij_H. 0 = 0 () where B .sxn is matrix of coefficients, its elements are functions of coordinates qi and velocities i =_1, . ,n is column vector of coefficients, its elements are functions of qi and qi, i = 1, . , n ii is column vector of generalized accelerations -nX 1 s is number of constraints of system n is number of holonomic coordinates. We suppose that the condition () is well-chosen