Radius of convergence of Lie series for some elliptic elements
Copyright policy )Radius of convergence of Lie series for some elliptic elements
For equatorial orbits about an oblate body, we show that the Lie series for the elliptic elementse,f,l and $$\varpi$$ diverge when the oblateness exceeds a critical multiple of the transformed eccentricity constant. The use of similar truncated series expansions for such elliptic elements by Brouwer accounts for the first-order errors at low eccentricity in his derived coordinates for an artificial satellite.
Lie series, artificial satellite problem, mean anomaly, polar co-ordinates, longitude of perifocus, true anomaly, elliptic orbital elements, Delaunay variables, von Zeipel method, expansions in terms of Poincare variables, D. Brouwer's solution, low eccentricity orbits, oblateness parameter, Astronomy and astrophysics, Celestial mechanics, Orbital mechanics, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
Lie series, artificial satellite problem, mean anomaly, polar co-ordinates, longitude of perifocus, true anomaly, elliptic orbital elements, Delaunay variables, von Zeipel method, expansions in terms of Poincare variables, D. Brouwer's solution, low eccentricity orbits, oblateness parameter, Astronomy and astrophysics, Celestial mechanics, Orbital mechanics, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
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