title: Statement and solution of a generalized Chebyshev problem. I
metadata.name: dc.contributor.author
metadata.value: Yushkov, Mikhail P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-12-06T13:26:14Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-12-06T13:26:14Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Yushkov M.P. Statement and solution of a generalized Chebyshev problem. I. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 4, pp. 680–701.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.413
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16751
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper gives a review of the research performed at the department of theoretical and
  applied mechanics for many years and devoted to solving the generalized Chebyshev problems.
  By a generalized Chebyshev problem is meant the problem in which the solution of
  a system of motion equations should simultaneously satisfy an additional system of highorder
  n ≥ 3 differential equations. Therefore, a new class of control problems is introduced positions can be named as an example of such devices. For solving a generalized Chebyshev
  problem it is offered to apply two theories of motion of nonholonomic systems with
  high-order constraints developed at the department of theoretical and applied mechanics of
  Saint Petersburg State University. In this case an additional system of differential equations
  is considered as a set of high-order programming constraints, the reaction forces of which
  prove to be the required control forces solving a generalized Chebyshev problem. The first
  theory is based on constructing a compatible system of differential equations with respect
  to the unknown generalized coordinates and Lagrange multipliers, the second one uses a
  generalized Gauss principle. Application of the theories is demonstrated by solving the
  problem on motion of the Earth satellite (a spacecraft) with a fixed value of acceleration.
  In the next paper with the same title the second theory will be applied for solving one of
  the most important problems of the control theory, the problem considering a mechanical
  system being transferred from one phase state to another in a given time.
  into consideration. A generalized Chebyshev problem is considered as an extension of the
  Chebyshev problem from the theory of synthesis of mechanisms in which it is required to
  construct a device the certain links of which should perform a required motion to some accuracy.
  The well-known Chebyshev mechanisms with stoppings of certain links at the given positions can be named as an example of such devices. For solving a generalized Chebyshev
  problem it is offered to apply two theories of motion of nonholonomic systems with
  high-order constraints developed at the department of theoretical and applied mechanics of
  Saint Petersburg State University. In this case an additional system of differential equations
  is considered as a set of high-order programming constraints, the reaction forces of which
  prove to be the required control forces solving a generalized Chebyshev problem. The first
  theory is based on constructing a compatible system of differential equations with respect
  to the unknown generalized coordinates and Lagrange multipliers, the second one uses a
  generalized Gauss principle. Application of the theories is demonstrated by solving the
  problem on motion of the Earth satellite (a spacecraft) with a fixed value of acceleration.
  In the next paper with the same title the second theory will be applied for solving one of
  the most important problems of the control theory, the problem considering a mechanical
  system being transferred from one phase state to another in a given time.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: nonholonomic mechanics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: high-order constraints
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Pontryagin maximum principle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generalized Gauss principle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: suppression of oscillation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generalized boundary problem
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Statement and solution of a generalized Chebyshev problem. I
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 680-701.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16751/1/680-701.pdf
resources.format: Adobe PDF
resources.size: 1,06 MB