On the motion of an Earth satellite after fixing the magnitude of its acceleration as a problem with nonholonomic third-order constraint

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Abstract

The motion of an artificial Earth satellite with constant absolute value of the acceleration is considered. This requirement is equivalent to imposing a second-order nonlinear nonholonomic constraint or a third-order linear nonholonomic constraint. Two theories of motion of nonholonomic systems with high-order constraints are used for solving this problem. According to the first theory, a consistent system of differential equations is constructed with respect to the generalized coordinates and the Lagrange multipliers; the second theory is based on the application of the generalized Gauss principle. The results are different, although the constraints are satisfied in both theories. It turns out that infinitely many solutions can be built, but using these theories one can find two specific solutions. The question of the difference of these two solutions from the set of all other possible solutions is raised. We also simplify the previously obtained differential equations. The transition to dimensionless variables is made. Three parameters of motion prior to imposition of the constraint are single out, which control the motion after the application of the constraint. The solutions obtained from these theories of motion of nonholonomic systems are compared.

Original languageEnglish
Article number012017
Number of pages8
JournalJournal of Physics: Conference Series
Volume1959
Issue number1
DOIs
StatePublished - 14 Jul 2021
EventInternational Scientific Conference on Mechanics "The Ninth Polyakhov's Reading", ISCM 2021 - Saint Petersburg, Russian Federation
Duration: 9 Mar 202112 Mar 2021

Scopus subject areas

  • Physics and Astronomy(all)

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