Ignorable Coordinates in the Ideal Resonance Problem

Details Ignorable Coordinates in the Ideal Resonance Problem Ignorable Coordinates in the Ideal Resonance Problem

Feb 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...7..205g&link_type=abstract

Celestial Mechanics, Volume 7, Issue 2, pp.205-224

Computer Science

12

Scientific paper

If a dynamical system ofN degrees of freedom is reduced to the Ideal Resonance Problem, the Hamiltonian takes the form F = B(y) + 2μ ^2 A(y)sin ^2 x_1 , μ<< 1. Herey is the momentum-vectory k withk=1, 2,...,N, andx 1 is thecritical argument. A first-orderglobal solution,x 1(t) andy 1(t), for theactive variables of the problem, has been given in Garfinkelet al. (1971). Sincex k fork>1 are ignorable coordinates, it follows that y_kappa = const., k > 1. The solution is completed here by the construction of the functionsx k(t) fork>1, derivable from the new HamiltonianF'(y') and the generatorS(x, y') of the von Zeipel canonical transformation used in the cited paper. The solution is subject to thenormality condition, derived in a previous paper fork=1, and extended here to 2≤k≤N. It is shown that the condition is satisfied in the problem of the critical inclination provided it is satisfied fork=1.

Affiliated with

Also associated with

No associations

Rating

Ignorable Coordinates in the Ideal Resonance 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 Ignorable Coordinates in the Ideal Resonance Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ignorable Coordinates in the Ideal Resonance Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1444801