caa a22 4500 445863463 CHVBK 20180317145450.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10569-011-9350-6 doi (NATIONALLICENCE)springer-10.1007/s10569-011-9350-6 The eleventh motion constant of the two-body problem [Elektronische Daten] [Andrew Sinclair, John Hurtado] The two-body problem is a twelfth-order time-invariant dynamic system, and therefore has eleven mutually-independent time-independent integrals, here referred to as motion constants. Some of these motion constants are related to the ten mutually-independent algebraic integrals of the n-body problem, whereas some are particular to the two-body problem. The problem can be decomposed into mass-center and relative-motion subsystems, each being sixth-order and each having five mutually-independent motion constants. This paper presents solutions for the eleventh motion constant, which relates the behavior of the two subsystems. The complete set of mutually-independent motion constants describes the shape of the state-space trajectories. The use of the eleventh motion constant is demonstrated in computing a solution to a two-point boundary-value problem. Springer Science+Business Media B.V., 2011 Two-body problem nationallicence Motion constants nationallicence Boundary-value problems nationallicence Sinclair Andrew Aerospace Engineering Department, Auburn University, 36849-5338, Auburn, AL, USA aut Hurtado John Aerospace Engineering Department, Texas A&M University, 77843-3141, College Station, TX, USA aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/3(2011-07-01), 189-198 0923-2958 110:3<189 2011 110 10569 https://doi.org/10.1007/s10569-011-9350-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-011-9350-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sinclair Andrew Aerospace Engineering Department, Auburn University, 36849-5338, Auburn, AL, USA aut NATIONALLICENCE 700 1- Hurtado John Aerospace Engineering Department, Texas A&M University, 77843-3141, College Station, TX, USA aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/3(2011-07-01), 189-198 0923-2958 110:3<189 2011 110 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer