On stationary solutions of some canonical systems of differential equations

Details On stationary solutions of some canonical systems of differential equations On stationary solutions of some canonical systems of differential equations

Nov 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25..297z&link_type=abstract

Celestial Mechanics, vol. 25, Nov. 1981, p. 297-315.

Mathematics

2

Canonical Forms, Differential Equations, Existence Theorems, Periodic Functions, Poincare Problem, Hamiltonian Functions, Matrices (Mathematics), Resonance, Steady State, Transformations (Mathematics)

Scientific paper

A method of constructing conditionally periodic solutions of canonical systems of differential equations with a quick-rotating phase is presented. The necessary conditions for the existence of the stationary solutions of such canonical systems are proved using Delaunay-Zeipel's transformation and Poincare's small parameter method. Symmetric solutions as distinct from asymmetric solutions in celestial mechanics are discussed, and all conclusions and estimates are considered to be correct for the systems striking at resonances.

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