# Hamiltonian structures of the first variation equations and symplectic connections

## Abstract

Necessary and sufficient conditions in terms of symplectic connections, ensuring that the first variation equation of a Hamiltonian system along a fixed invariant symplectic submanifold is also a Hamiltonian system with respect to some admissible symplectic structure are obtained. The class of admissible symplectic structures is distinguished by means of the natural condition of compatibility with the symplectic 2-form in the ambient space. Possible obstructions to the existence of a Hamiltonian structure on the first variation equation are investigated.

- Authors:

- Moscow State Institute of Electronics and Mathematics - Technical University, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21202923

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 191; Journal Issue: 4; Other Information: DOI: 10.1070/SM2000v191n04ABEH000468; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPATIBILITY; EQUATIONS; HAMILTONIANS; MATHEMATICAL SPACE; VARIATIONS

### Citation Formats

```
Vorob'ev, Yu M.
```*Hamiltonian structures of the first variation equations and symplectic connections*. United States: N. p., 2000.
Web. doi:10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Vorob'ev, Yu M.
```*Hamiltonian structures of the first variation equations and symplectic connections*. United States. doi:10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).

```
Vorob'ev, Yu M. Sun .
"Hamiltonian structures of the first variation equations and symplectic connections". United States. doi:10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
```

```
@article{osti_21202923,
```

title = {Hamiltonian structures of the first variation equations and symplectic connections},

author = {Vorob'ev, Yu M},

abstractNote = {Necessary and sufficient conditions in terms of symplectic connections, ensuring that the first variation equation of a Hamiltonian system along a fixed invariant symplectic submanifold is also a Hamiltonian system with respect to some admissible symplectic structure are obtained. The class of admissible symplectic structures is distinguished by means of the natural condition of compatibility with the symplectic 2-form in the ambient space. Possible obstructions to the existence of a Hamiltonian structure on the first variation equation are investigated.},

doi = {10.1070/SM2000V191N04ABEH000468; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 4,

volume = 191,

place = {United States},

year = {2000},

month = {4}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.