The Ideal Resonance Problem: A comparison of the solutions expressed in terms of mean elements and in terms of initial conditions

1974 ◽  
Vol 8 (4) ◽  
pp. 523-530 ◽  
Author(s):  
Alan H. Jupp
Keyword(s):  
Initial Conditions ◽  
Resonance Problem ◽  
Ideal Resonance ◽  
Ideal Resonance Problem ◽  
Mean Elements ◽  
The Ideal

scholarly journals A Comparison of the Mean-Value and Initial-Value Solutions of the Ideal Resonance Problem with an Application in Rigid-Body Mechanics

1974 ◽  
Vol 62 ◽  
pp. 209-209
Author(s):  
A. H. Jupp
Keyword(s):  
Elliptic Functions ◽  
Mean Value ◽  
Resonance Problem ◽  
Ideal Resonance ◽  
Deep Circulation ◽  
Ideal Resonance Problem ◽  
Rigid Body Mechanics ◽  
The Mean ◽  
Mean Elements ◽  
The Ideal

A solution of the ideal resonance problem has already been exhibited (Jupp, 1972) 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 motions on or close to the separatrix of the phase plane of the dynamical system.

A second-order global solution of the ideal resonance problem

1974 ◽  
Vol 9 (1) ◽  
pp. 105-125 ◽  
Author(s):  
Boris Garfinkel ◽  
Carol A. Williams
Keyword(s):  
Global Solution ◽  
Second Order ◽  
Resonance Problem ◽  
Ideal Resonance ◽  
Ideal Resonance Problem ◽  
The Ideal

Erratum: A Recursive von Zeipel Algorithm for the Ideal Resonance Problem

1971 ◽  
Vol 76 ◽  
pp. 581
Author(s):  
Boris Garfinkel ◽  
Alan Jupp ◽  
Carol Williams
Keyword(s):  
Resonance Problem ◽  
Ideal Resonance ◽  
Ideal Resonance Problem ◽  
The Ideal
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