Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, March 25, 2003, final revision, February 6, 2004. Associate Editor: I. Mezic.

In Lagrangian mechanics, under certain conditions, the Jacobi energy integral exists and plays a fundamental role (see 1,2,3,4,5,6). More generally, when Jacobi’s integral does not exist, it is still possible to gain useful engineering information from a consideration of power versus rate-of-energy relations. In the present note, we are concerned with a system of $N ⩾1$ particles subject to general holonomic and non-holonomic constraints. The unconstrained physical system may be represented by an abstract particle P in a $3N$-dimensional Euclidean configuration space. In the presence of holonomic constraints, the motion of P is...