Properties of solutions of nonlinear equations of mechanics control systems

Research output

1 Citation (Scopus)

Abstract

Particularities of the application of the equations of motion in gravitational fields in nonlinear problems to problems, when equations or solutions contain nonsmooth functions, are discussed. Classical mechanics is engaged in the study of properties, approximation and prediction of motion for problems with regular functions. Solving nonlinear equations of dynamics uses additional transformations to eliminate singularities of equations for complex systems that lead to a linear or simplified form. This gives the possibility of solving with regard to the stages of successive approximation. The application of such transformations is considered for solving the problems of controlled motion of space vehicles in the gravitational field, taking into account active and reactive forces. After reduction to the canonical form or regular elements of nonlinear equations of dynamics we obtain the initial approximation. The control by the relay view determines the switching times at corner points based on the Pontryagin maximum principle. It is required to join successive sections of the trajectory.

Original languageEnglish
Title of host publication2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781509062607
DOIs
Publication statusPublished - 10 Jul 2017
Event2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017: dedicated to the Memory of V.F. Demyanov - Saint-Petersburg
Duration: 21 May 201726 May 2017
http://www.pdmi.ras.ru/EIMI/2017/CNSA/

Conference

Conference2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017
Abbreviated titleCNSA 2017
CountryRussian Federation
CitySaint-Petersburg
Period21/05/1726/05/17
Internet address

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Nonlinear equations
Mechanics
Nonlinear Equations
Control System
Gravitational Field
Control systems
Maximum principle
Equations of motion
Large scale systems
Regular Element
Nonsmooth Function
Pontryagin Maximum Principle
Motion
Classical Mechanics
Successive Approximation
Trajectories
Approximation Property
Canonical form
Relay
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Scopus subject areas

  • Modelling and Simulation
  • Analysis
  • Applied Mathematics
  • Control and Optimization

Cite this

Korolev, V. (2017). Properties of solutions of nonlinear equations of mechanics control systems. In 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings [7973973] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CNSA.2017.7973973
Korolev, Vladimir. / Properties of solutions of nonlinear equations of mechanics control systems. 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017.
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Korolev, V 2017, Properties of solutions of nonlinear equations of mechanics control systems. in 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings., 7973973, Institute of Electrical and Electronics Engineers Inc., Saint-Petersburg, 21/05/17. https://doi.org/10.1109/CNSA.2017.7973973

Properties of solutions of nonlinear equations of mechanics control systems. / Korolev, Vladimir.

2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. 7973973.

Research output

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N2 - Particularities of the application of the equations of motion in gravitational fields in nonlinear problems to problems, when equations or solutions contain nonsmooth functions, are discussed. Classical mechanics is engaged in the study of properties, approximation and prediction of motion for problems with regular functions. Solving nonlinear equations of dynamics uses additional transformations to eliminate singularities of equations for complex systems that lead to a linear or simplified form. This gives the possibility of solving with regard to the stages of successive approximation. The application of such transformations is considered for solving the problems of controlled motion of space vehicles in the gravitational field, taking into account active and reactive forces. After reduction to the canonical form or regular elements of nonlinear equations of dynamics we obtain the initial approximation. The control by the relay view determines the switching times at corner points based on the Pontryagin maximum principle. It is required to join successive sections of the trajectory.

AB - Particularities of the application of the equations of motion in gravitational fields in nonlinear problems to problems, when equations or solutions contain nonsmooth functions, are discussed. Classical mechanics is engaged in the study of properties, approximation and prediction of motion for problems with regular functions. Solving nonlinear equations of dynamics uses additional transformations to eliminate singularities of equations for complex systems that lead to a linear or simplified form. This gives the possibility of solving with regard to the stages of successive approximation. The application of such transformations is considered for solving the problems of controlled motion of space vehicles in the gravitational field, taking into account active and reactive forces. After reduction to the canonical form or regular elements of nonlinear equations of dynamics we obtain the initial approximation. The control by the relay view determines the switching times at corner points based on the Pontryagin maximum principle. It is required to join successive sections of the trajectory.

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Korolev V. Properties of solutions of nonlinear equations of mechanics control systems. In 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. 7973973 https://doi.org/10.1109/CNSA.2017.7973973