An energy principle to find the equations of motion is outlined within the scope of continuum classical mechanics and compared with the very useful and widely applied Hamilton's Principle. It is shown that to obtain convenient results by means of the latter principle, a strong restriction on the variations of the functions of interest must be accepted. Furthermore, such restrictions are confronted with the ones that, at the same time, derive from the manipulation of the principle herein proposed. Two illustrative examples are also included.
Bailey, C.D., 1975, "A new look at Hamilton's Principle," Foundations of Physics5(3), 433-451.
2.
Filipich, C.P., Maurizi, M.J., and Rosales, M.B., 1987, "Free vibrations of a spinning uniform beam with ends elastically restrained against rotation," Journal of Sound and Vibration116(3), 475-482.
3.
Filipich, C.P. and Rosales, M.B., 1992, "Exact frequencies of beams and plates: A generalized solution." in Proceedings of the International Congress on Numerical Methods in Engineering and Applied Sciences I, Concepción , Chile, November 16-20, 307-316.
4.
Filipich, C.P. and Rosales, M.B., 1994, "Beams and arcs: Exact values of frequencies via a generalized solution," Journal of Sound and Vibration170(2), 263-269.
5.
Filipich, C.P. and Rosales, M.B., 1995, " Alternative approach for the exact solution of the forced vibration of beams," Applied Mechanics Review48(11) part 2, 596-5101.
6.
Fung, Y.C., 1968. Foundations of Solid Mechanics, Prentice-Hall , New Delhi.
7.
Rajan, M. and Junkins, J.L., 1983, "Perturbation methods based upon varying action integrals ," International Journal of Non-Linear Mechanics18(5), 335-351.
8.
Truesdell, C.A. and Toupin, R.A., 1954, The Classical Field Theories, Encyclopedia of Physics , Flügge, ed., Springer-Veriag , Berlin.
9.
Vujanovic, B., 1978, "Conservation laws of dynamical systems via D'Alembert's principle," International Journal of NonLinear Mechanics13, 185-197.
