tailieunhanh - Principle of compatibility and non-generalised coordinates

In the article the author derived the theoretical basis as well as numerical algorithms concerning the combination of nongeneralised coordinates with the principle of compatibility. Some comparisons of the technique under consideration and usual technique using Lagrange multipliers are discussed. Some examples are shown for illustration. The case of contact of moving disc on the surface is given in detail | Vietnam Journal of Mechanics, Vol. 27, No. 2 (2005 ), pp. 74 - 85 PRINCIPLE OF COMPATIBILITY AND NON-GENERALISED COORDINATES DINH VAN PHONG Hanoi University of Technology Abstract. The contribution is devoted to using so-called non-generalised coordinates for deriving the system of equations of motion. Differently from common techniques for constrained mechanical systems the principle of compatibility is chosen as the tool. This takes the advantage in the possibility for extension to systems with nonideal constraints, however, the special treatment is needed. In the article the author derived the theoretical basis as well as numerical algorithms concerning the combination of nongeneralised coordinates with the principle of compatibility. Some comparisons of the technique under consideration and usual technique using Lagrange multipliers are discussed. Some examples are shown for illustration. The case of contact of moving disc on the surface is given in detail 1. INTRODUCTION As known the configuration and the motion of mechanical systems are described by a set of coordinates. Various coordinate systems can be used, therefore the sets of coordinates and equations of motion are different to each other. Commonly we can call them, regardless to the physical meaning, as generalised coordinates and use them for deriving equations of motion. Since generalised coordinates describe the configuration of mechanical system, each coordinate is related to the mass properties of the system. For each coordinate we dispose of one equation of motion in the form of a differential equation of second order. Therefore, if the system is determined by n generalised coordinates we get the system of n differential equations. Obviously, if these coordinates are not independent, the constraint equations are added to the existing system of differential equations. The system is called the constrained mechanical system, see . [1], [4], [9], [17], [24], [27] etc. In engineering .