zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some initial conditions for disposed satellites of the systems GPS and Galileo constellations. (English) Zbl 1185.86025
Summary: Through the averaged equations we revisit theoretical and numerical aspects of the strong resonance that increases the eccentricity of the disposed objects of GPS and Galileo Systems. A simple view of the phase space of the problem shows that the resonance does not depend on the semi-major axis. Therefore, usual strategies of changing altitude (raising perigee) do not work. In this problem we search for a set of initial conditions such that the deactivated satellites or upper-stages remain at least for 250 years without penetrating in the orbits of the operational satellites. In the case that Moon’s perturbation is not significant, we can identify, in the phase space, the regions where eccentricity reaches maximum and minimum values so that possible risks of collision can be avoided. This is done semi-analytically through the averaged system of the problem. Guided by this idea, we numerically found the (ω,Ω) values of the real unaveraged problem. In particular, for the Galileo case, the theoretical results predicted in the averaged system are in good agreement with numerical results. We also show that initial inclination of the Moon plays an important role in the search of these conditions.
86A30Geodesy, mapping problems
70F15Celestial mechanics