A new viewpoint is suggested for expressing the governing equations of analytical mechanics. This viewpoint establishes a convenient framework for examining the relationships among Lagrange’s equations, Hamilton’s equations, and Kane’s equations. The conditions which must be satisfied for the existence of an energy integral in the context of Kane’s equations are clarified, and a generalized form of Hamilton’s Principle is presented. Generalized speeds replace generalized velocities as the velocity variables in the formulation. The development considers holonomic systems in which the generalized forces are derivable from a potential function.

Issue Section:
Technical Papers
Topics:
Hamilton's principle, Variational principles
1.
Athans, M., and Falb, P. L., 1966, Optimal Control, McGraw-Hill, New York.
2.
Bryson, A. E., and Ho, Y. C., 1975, Applied Optimal Control, Halstead Press, New York.
3.
Gelfand, I. M., and Fomin, S. V., 1963, Calculus of Variations, Prentice-Hall, Englewood Cliffs, NJ.
4.
Hamilton, W. R., 1834, “On a General Method in Dynamics,” Philosophical Transactions, pp. 247–308.
5.
Hughes, P. C., 1986, Spacecraft Attitude Dynamics, John Wiley and Sons, New York.
6.
Kane, T. R., and Levinson, D. A., 1985, Dynamics Theory and Applications, McGraw-Hill, New York.
7.
Kane
T. R.
, and
Levinson
D. A.
,
1990
, “
Testing Numerical Integrations of Equations of Motions
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
57
, pp.
248
–
249
.
8.
Meirovitch, L., 1970, Methods of Analytical Dynamics, McGraw-Hill, New York, pp. 157–160.
9.
Pars, 1979, A Treatise on Analytical Dynamics, Ox Bow Press, Wood-bridge, CT.
10.
Whittaker, E. T., 1964, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, London.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.