This paper presents a kinetic energy theorem, applicable with simple nonholonomic systems. The theorem provides a basis for developing testing functions for measuring the accuracy of numerical simulations—even where no classical conservation principle is applicable. The theorem is established using Kane’s equations for general mechanical systems. A set of general testing functions are then developed. Several examples are presented.

1.
Kane
T. R.
, and
Banerjee
A. K.
,
1983
, “
A Conservation Theorem for Simple Nonholonomic Systems
,”
ASME Journal of Applied Mechanics
, Vol.
50
, pp.
647
651
.
2.
Kane, T. R., and Levinson, D. A., 1985, Dynamics: Theory and Applications, McGraw Hill, New York, p. 50, 102.
3.
Kane
T. R
, and
Levinson
D. A.
,
1988
, “
A Method for Testing Numerical Integrations of Equations of Motion of Mechanical Systems
,”
ASME Journal of Applied Mechanics
, Vol.
55
, pp.
711
715
.
4.
Kane
T. R.
, and
Levinson
D. A.
,
1990
, “
Testing Numerical Integrations of Equations of Motion
,”
ASME Journal of Applied Mechanics
, Vol.
57
, pp.
248
249
.
5.
Neimark, J. I., and Fufaev, N. A., 1972, Dynamics of Nonholonomic Systems, American Mathematical Society, Providence, RI, pp. 120–128, 131–135.
6.
Papastavridis
J. G.
,
1991
, “
On Energy Rate Theorems for Linear First-Order Nonholonomic Systems
,”
ASME Journal of Applied Mechanics
, Vol.
58
, pp.
536
544
.
7.
Souchet
R.
,
1991
, “
A New Expression of the Energy Theorem in Discrete Mechanical Systems
,”
ASME Journal of Applied Mechanics
, Vol.
58
, pp.
1086
1088
.
8.
Wang, J. T., 1992, “A Conservation Theorem for Constrained Multibody Systems,” General Motors Research Laboratories Technical Report No. GMR-7627 (to be published in ASME Journal of Applied Mechanics).
This content is only available via PDF.
You do not currently have access to this content.