THE GENERAL EQUATIONS OF ANALYTICAL DYNAMICS

It is shown that the generalized Poincare and Chetayev equations, whic h represent the equations of motion of mechanical systems using a cert ain closed system of infinitesimal linear operators, are related to th e fundamental equations of analytical dynamics. Equations are derived in quasi-coordinates for the case of redundant variables; it is shown that when an energy integral exists the operator X-0 = delta/delta t s atisfies the Chetayev cyclic-displacement conditions. Using the energy integral the order of the system of equations of motion is reduced, a nd generalized Jacobi-Whittaker equations are derived from the Chetaye v equations. It is shown that the Poincare-Chetayev equations are equi valent to a number of equations of motion of non-holonomic systems, in particular, the Maggi, Volterra, Kane, and so on, equations. On the b asis of these, and also of other previously obtained results, the Poin care and Chetayev equations in redundant variables, applicable both to holonomic and non-holonomic systems, can be regarded as general equat ions of classical dynamics, equivalent to the well-known fundamental f orms of the equations of motion,a number of which follow as special ca ses from the Poincare and Chetayev equations. (C) 1997 Elsevier Scienc e Ltd.