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- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Dynamical Systems and Ergodic Theory
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/S1560354709010043
- Publisher site
- See Article on Publisher Site
Abstract
Systems of material points interacting both with one another and with an external field are considered in Euclidean space. For the case of arbitrary binary interaction depending solely on the mutual distance between the bodies, new integrals are found, which form a Galilean momentum vector. A corresponding algebra of integrals constituted by the integrals of momentum, angular momentum, and Galilean momentum is presented. Particle systems with a particle-interaction potential homogeneous of degree α = −2 are considered. The most general form of the additional integral of motion, which we term the Jacobi integral, is presented for such systems. A new nonlinear algebra of integrals including the Jacobi integral is found. A systematic description is given to a new reduction procedure and possibilities of applying it to dynamics with the aim of lowering the order of Hamiltonian systems.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Feb 10, 2009