On the Third Integral of the Galaxy

Details On the Third Integral of the Galaxy On the Third Integral of the Galaxy

Jan 1968

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1968ap%26ss...1....6g&link_type=abstract

Astrophysics and Space Science, Volume 1, Issue 1, pp.6-19

Astronomy and Astrophysics

Astrophysics

3

Scientific paper

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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