Forms of Hamilton's principle in quasi-coordinates

In a previous paper [1], certain conditions, due to Holder, Voronets and Su slov in the case of linear constraints, for deriving three forms of Hamilto n's principle in generalized coordinates and velocities for the general cas e of non-linear non-holonomic constraints were analysed. It was shown that these three forms are equivalent and transform into one another. As a seque l to that analysis, similar issues are investigated for the case of non-lin ear quasi-coordinates and quasi-velocities and, in addition, the three form s of Hamilton's principle are exhibited in the case of a Legendre transform ation, which transforms the equation of motion to canonical form in quasi-c oordinates. (C) 1999 Elsevier Science Ltd. All rights reserved.