### 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 language | English |
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Title of host publication | 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781509062607 |

DOIs | |

Publication status | Published - 10 Jul 2017 |

Event | 2017 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 2017 → 26 May 2017 http://www.pdmi.ras.ru/EIMI/2017/CNSA/ |

### Conference

Conference | 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 |
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Abbreviated title | CNSA 2017 |

Country | Russian Federation |

City | Saint-Petersburg |

Period | 21/05/17 → 26/05/17 |

Internet address |

### Fingerprint

### Scopus subject areas

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

### Cite this

*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

}

*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.

Research output

TY - GEN

T1 - Properties of solutions of nonlinear equations of mechanics control systems

AU - Korolev, Vladimir

PY - 2017/7/10

Y1 - 2017/7/10

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.

UR - http://www.scopus.com/inward/record.url?scp=85027456070&partnerID=8YFLogxK

U2 - 10.1109/CNSA.2017.7973973

DO - 10.1109/CNSA.2017.7973973

M3 - Conference contribution

AN - SCOPUS:85027456070

BT - 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -