Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cemda..73..139m&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 73, Issue 1/4, p. 139-147 (1999).
Astronomy and Astrophysics
Astronomy
2
Chaos, Phase Space, Lagrangian Displacements
Scientific paper
The gravitational n-body problem is chaotic. Phase trajectories that start very near each other separate rapidly. The rate looks exponential over long times. At any instant, trajectories separated in certain directions move apart rapidly (unstable directions), while those separated in other directions stay about the same (stable directions). Unstable directions lie along eigenvectors that correspond to positive eigenvalues of the matrix of force gradients. The number of positive eigenvalues of that matrix gives the dimensionality of stable regions. This number has been studied numerically in a series of 100-body integrations. It continues to change as long as the integration continues because the matrix changes extremely rapidly. On average, there are about 1.2n unstable directions out of 3n. Issues of dimensionality arise when the tools of ergodic studies are brought to bear on the problem of trajectory separation. A method of estimating the rate of trajectory separation based on matrix descriptions is presented in this note. Severe approximations are required.
No associations
LandOfFree
Dimensionality of Stable and Unstable Directions in the Gravitational N-Body Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dimensionality of Stable and Unstable Directions in the Gravitational N-Body Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dimensionality of Stable and Unstable Directions in the Gravitational N-Body Problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1190573