ON THE POINCARE-CHETAYEV EQUATIONS

It is proved that, under fairly general conditions, the canonical Poin care-Chetayev equations are Hamiltonian equations in non-canonical var iables. It is shown that systems of generalized Lagrange and Hamilton equations in redundant variables, of lower order than equations that c ontain undetermined multipliers, as well as the Euler-Lagrange equatio ns in quasi-coordinates, are all special cases of the Poincare-Chetaye v equations. Thus the theory of the latter extends at once to the type s of systems just listed. The problem of using the Poincare-Chetayev e quations in non-holonomic dynamics is discussed.