Abstract
It is shown here that the ‘third integral’ of the galaxy, whenever its constant is conserved, defines the same surface as the Hamiltonian, and thus does not constitute anynew integral, but a function of the already known integral of energy. In particular, the ‘third integral’ and the Hamiltonian are found to possess collinear gradients, in accordance with Poincaré's theorem concerning the characteristic exponents in systems with multiple integrals.
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Goudas, C.L. On the third integral of the galaxy. Astrophys Space Sci 1, 6–19 (1968). https://doi.org/10.1007/BF00653843
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DOI: https://doi.org/10.1007/BF00653843