The problem of the Eulerian oscillations: A weakness of numerical versus analytical methods |
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| Authors: | Odile Calame J Derral Mulholland |
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| Institution: | (1) CERGA, Avenue Copernic, 06130 Grasse, FRANCE;(2) CERGA and Space Astronomy Laboratory, 32609 Gainesville, Florida, USA |
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| Abstract: | The application of computer technology has permitted more and more problems of dynamical astronomy to be solved more easily, quickly, and accurately. In this area, numerical integration is often very efficient, and sometimes essential. There is often, however, a temptation to choose numerical integration simply because it is the easiest way to attack the problem. Sometimes this works to the detriment of a satisfactory understanding of the physics of the problem under study. It is particularly the case for the  free , or Eulerian, oscillations. The forces that create such a motion are not of gravitational origin and are not even conservative. The theory can only specify the frequencies of oscillation, not their amplitudes nor phases. The case is complicated when the free oscillations interact with gravitationally-forced oscillations, a situation that is almost inevitable, since nothing is isolated in the Universe. The first author has particularly studied this problem in the case of the rotation of the Moon, and published the first credible determinations of the lunar free libration. In this kind of problem, the observations have to be used and care must to be taken to create no spurious free librations in the results by using numerical integrations to describe the other related motions. A differential correction of the starting conditions to fit the observations does not necessarily give any valid information on the real free oscillation contained in the data. An analytical model is necessary, if the goal of the research is to understand the origins and characteristics of an Eulerian oscillation in such a system. |
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