The Poincaré-Chetayev equations and flexible multibody systems

Problems of the dynamics of flexible multibody systems (FMBSs) and its relation to the fundamental system of equations obtained by Poincaré about 100 years ago [1] are considered. These equations, called the Poincaré-Chetayev equations, are now well known as the basis of the Lagrange reduction theory. By extending these equations to the case of the motion of a Cosserat medium it is shown that in the dynamics of FMBS it is possible to use two principal systems of equations. It is proved that a generalized Newton-Euler model of FMBSs in projections onto floating axes and the partial differential equations of the non-linear, geometrically exact theory within the Galilean approach comprise the Poincaré-Chetayev equations.