The Ideal Resonance Problem: A Comparison of the Solutions Expressed in Terms of Mean Elements and in Terms of Initial Conditions

Details The Ideal Resonance Problem: A Comparison of the Solutions Expressed in Terms of Mean Elements and in Terms of Initial Conditions The Ideal Resonance Problem: A Comparison of the Solutions Expressed in Terms of Mean Elements and in Terms of Initial Conditions

Jan 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec...8..523j&link_type=abstract

Celestial Mechanics, Volume 8, Issue 4, pp.523-530

Physics

8

Scientific paper

In an earlier publication (Jupp, 1972), a solution of the Ideal Resonance Problem is exhibited explicitly in terms of the ‘mean’ elements; to second order in the small parameter in the case of libration, and to first order in the case of deep circulation. Both representations possess a singularity when the ‘mean’ modulus of the Jacobi elliptic functions is unity; this corresponds to the separatrix of the phase plane of the dynamical system. It is shown here that, provided particular coefficients associated with the problem satisfy specific relations, the singularity is removed, and the resulting solution is applicable throughout the deep resonance region. The solution is then expressed in terms of general initial conditions. Again, in general, the solution has a singularity associated closely with the limiting motion, and the circulation part of the solution is restricted to deep circulation. It is shown that when the previously-mentioned coefficients satisfy particular constraints, the singularity is removed. In addition, with the same constraints, the deep-circulation solution is applicable throughout the circulation region. It is of interest that these constraints are quite different from those associated with the ‘mean’, element formulation.

Affiliated with

Also associated with

No associations

Rating

The Ideal Resonance Problem: A Comparison of the Solutions Expressed in Terms of Mean Elements and in Terms of Initial Conditions 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 The Ideal Resonance Problem: A Comparison of the Solutions Expressed in Terms of Mean Elements and in Terms of Initial Conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Ideal Resonance Problem: A Comparison of the Solutions Expressed in Terms of Mean Elements and in Terms of Initial Conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1840402