Normality Condition in the Ideal Resonance Problem

Details Normality Condition in the Ideal Resonance Problem Normality Condition in the Ideal Resonance Problem

Sep 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972cemec...6..151g&link_type=abstract

Celestial Mechanics, Volume 6, Issue 2, pp.151-166

Physics

14

Scientific paper

The Ideal Resonance Problem, defined by the Hamiltonian F = B(y) + 2μ ^2 A(y)sin ^2 x,μ ≪ 1, has been solved in Garfinkelet al. (1971). As a perturbed simple pendulum, this solution furnishes a convenient and accurate reference orbit for the study of resonance. In order to preserve the penduloid character of the motion, the solution is subject to thenormality condition, which boundsAB" andB' away from zero indeep and inshallow resonance, respectively. For a first-order solution, the paper derives the normality condition in the form pi ≤slant max(|α /α _1 |,|α /α _1 |^{2i} ),i = 1,2. Herep i are known functions of the constant ‘mean element’y', α is the resonance parameter defined by α equiv - B'/|4AB' ' |^{1/2} μ , and α _1 equiv μ ^{ - 1/2} defines the conventionaldemarcation point separating the deep and the shallow resonance regions. The results are applied to the problem of the critical inclination of a satellite of an oblate planet. There the normality condition takes the form Λ _1 (λ ) ≤slant e ≤slant Λ _2 (λ )if|i - tan^{ - 1} 2| ≤slant λ e/2(1 + e) withΛ 1, andΛ 2 known functions of λ, defined by begin{gathered} λ equiv |tfrac{1}{5}(J_2 + J_4 /J_2 )|^{1/4} /q, \ q equiv a(1 - e). \

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-986924