Mathematics
Scientific paper
Feb 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..21..203r&link_type=abstract
(Conference on Mathematical Methods in Celestial Mechanics, 6th, Oberwolfach, West Germany, Aug. 14-19, 1978.) Celestial Mechani
Mathematics
Canonical Forms, Celestial Mechanics, Eigenvalues, Euler Equations Of Motion, Transformations (Mathematics), Hamiltonian Functions, Linear Equations, Matrices (Mathematics)
Scientific paper
The Euler-Poinsot problem is considered with a view towards the perturbation theory which deals with the rotation of the earth or the physical libration of the moon. A general matrix was sought that would solve the problem of normalization (eigenvalues different from zero), then an attempt was made to fix the arbitrary coefficients to get a symplectic matrix. There was not found to exist, however, an appropriate symplectic matrix which normalizes the equation of motion, and the perturbation theory thus seems to lose the Hamiltonian character in the Euler-Poinsot problem. On the other hand, introducing the first integral G (of the Hamiltonian) has the effect of changing the linear equations, and the normalization is shown to be possible in this case.
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