"planetary theory" .
"variation curve" .
"variables" .
_:N1777aff62954425691de11077283b1a6 "10.1007/978-94-010-3323-7_37" .
.
_:N1f0c97aafa7448adabbbbce52e4418fb .
"inclination" .
"function" .
"solution" .
_:N3352caeb774240e38934424c28c7bcab .
.
"motion" .
"system" .
"Mathematical Sciences" .
"Brumberg" .
"https://doi.org/10.1007/978-94-010-3323-7_37" .
"This paper suggests an algorithm for the formal solution of the N planet problem in the rectangular heliocentric coordinates. The algorithm is based on the use of the intermediate quasiperiodic solution generalizing the variation curve of Hill. This particular solution is expressed by power series in terms of the planetary masses with quasi-periodic coefficients. It contains all the inequalities that do not depend on the orbital eccentricities and inclinations. The system of the nonlinear differential equations for the deviations of the true values of the coordinates from those corresponding to the intermediate solution has been further derived. The solution of this system is presented by the series in powers of the variables slowly changing with the time. The coefficients of these series are quasi-periodic functions dependent on the mean longitudes of the planets and developable in powers of the planetary masses. The behaviour of the slowly changing variables is described by the autonomous system of the nonlinear differential equations. This final system yields the secular perturbations in the planetary motion." .
.
_:Nadd127d79ed040a9b52a439e4e32123b .
"series" .
"general planetary theory" .
"1970-01-01" .
_:N3dc10770be0d4f65bebf89bcd39f3573 .
_:N1f0c97aafa7448adabbbbce52e4418fb .
"coordinates" .
"true value" .
"method" .
"values" .
_:N1f0c97aafa7448adabbbbce52e4418fb _:Ndab1f50347d842a497a2a21993fbc999 .
.
_:N3dc10770be0d4f65bebf89bcd39f3573 .
_:Nadd127d79ed040a9b52a439e4e32123b .
.
.
"410-450" .
"intermediate quasiperiodic solution" .
"Pure Mathematics" .
"formal solution" .
_:N3dc10770be0d4f65bebf89bcd39f3573 "pub.1005622088" .
"lunar method" .
"deviation" .
"en" .
"eccentricity" .
"orbital eccentricity" .
"chapters" .
.
"https://scigraph.springernature.com/explorer/license/" .
"algorithm" .
"coefficient" .
"Institute of Theoretical Astronomy, Leningrad, U.S.S.R." .
.
"autonomous systems" .
"Hill\u2019s Lunar Method" .
"differential equations" .
"secular perturbations" .
"chapter" .
_:N63e13378aee24f52b232f9a5c2fde899 "Springer Nature" .
"equations" .
.
"longitude" .
"nonlinear differential equations" .
"power" .
_:N516b6d0afd794638ab7869f51d13d297 .
_:N3352caeb774240e38934424c28c7bcab .
"terms" .
_:N1777aff62954425691de11077283b1a6 .
.
_:N3352caeb774240e38934424c28c7bcab "Springer Nature - SN SciGraph project" .
"Application of Hill\u2019s Lunar Method in General Planetary Theory" .
"rectangular heliocentric coordinates" .
.
_:N516b6d0afd794638ab7869f51d13d297 .
_:Ndab1f50347d842a497a2a21993fbc999 "Giacaglia" .
"Hill" .
"curves" .
"planetary motion" .
_:Nadd127d79ed040a9b52a439e4e32123b "978-94-010-3323-7" .
"problem" .
"quasi-periodic coefficients" .
_:N63e13378aee24f52b232f9a5c2fde899 .
"theory" .
_:Nadd127d79ed040a9b52a439e4e32123b "Periodic Orbits, Stability and Resonances" .
"mass" .
"power series" .
.
"mean longitude" .
"false"^^ .
_:N1777aff62954425691de11077283b1a6 .
"paper" .
"applications" .
"quasi-periodic functions" .
"particular solutions" .
"time" .
_:N516b6d0afd794638ab7869f51d13d297 .
_:N1777aff62954425691de11077283b1a6 "doi" .
"use" .
_:Ndab1f50347d842a497a2a21993fbc999 .
"heliocentric coordinates" .
"Institute of Theoretical Astronomy, Leningrad, U.S.S.R." .
"planetary mass" .
"2021-11-01T18:52" .
"planets" .
_:Ndab1f50347d842a497a2a21993fbc999 "G. E. O." .
.
"final system" .
"1970" .
"intermediate solution" .
"perturbations" .
_:N3dc10770be0d4f65bebf89bcd39f3573 "dimensions_id" .
"V. A." .
.
"planet problem" .
_:N63e13378aee24f52b232f9a5c2fde899 .
"inequality" .
"quasiperiodic solutions" .
_:Nadd127d79ed040a9b52a439e4e32123b "978-94-010-3325-1" .
"behavior" .