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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On the motion of an Earth satellite after fixing the magnitude of its acceleration as a problem with nonholonomic third-order constraint. / Dodonov, V. V.; Kozlova, A. S. .

In: Journal of Physics: Conference Series, Vol. 1959, No. 1, 012017, 01.07.2021.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{90a02fcf6bcc43eebe277ba1fe334558,

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

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.",

author = "Dodonov, {V. V.} and Kozlova, {A. S.}",

note = "Publisher Copyright: {\textcopyright} 2021 Published under licence by IOP Publishing Ltd.; International Scientific Conference on Mechanics {"}The Ninth Polyakhov's Reading{"}, ISCM 2021 ; Conference date: 09-03-2021 Through 12-03-2021",

year = "2021",

month = jul,

day = "1",

doi = "10.1088/1742-6596/1959/1/012017",

language = "English",

volume = "1959",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - On the motion of an Earth satellite after fixing the magnitude of its acceleration as a problem with nonholonomic third-order constraint

AU - Dodonov, V. V.

AU - Kozlova, A. S.

PY - 2021/7/1

Y1 - 2021/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85111963188&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1959/1/012017

DO - 10.1088/1742-6596/1959/1/012017

M3 - Conference article

AN - SCOPUS:85111963188

VL - 1959

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012017

T2 - International Scientific Conference on Mechanics "The Ninth Polyakhov's Reading", ISCM 2021

Y2 - 9 March 2021 through 12 March 2021

ER -

ID: 86230536