On the Poincare and Chetayev equations

The Lie group of virtual displacement operators in Rodrigues-Hamilton param eters is constructed and equations of motion are derived for a heavy rigid body with one fixed point. It is shown that the addition (subtraction) of a term of the form df/dt, f(t, x) is an element of C-2, to (from) the genera lized Lagrangian L*(t, x, eta) does not affect the form of the Poincare and Chetayev equations. These equations can also be used to describe the relat ive motion of a holonomic system relative to a moving system of coordinates . Hamel's equations in non-linear quasi-coordinates are derived without usi ng the transitivity equations, are compared with the generalized Poincare e quations and are transformed to Chetayev canonical form. (C) 1998 Elsevier Science Ltd. All rights reserved.