The Third Integral and The Hamiltonian

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Scientific paper

It is reiterated that any suggestion of the existence of a ‘third integral’ is at variance with Poincaré's theorem on the non-existence of such integrals. Even in a purely numerical approach no form of a new ‘integral’ can be constructed that is valid in every domain of the phase space; and it is devoid of meaning to use as a ‘third integral’ different forms of functions in various cases.

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