Lie transforms: A perspective

2005 ◽  
pp. 63-86 ◽  
Author(s):  
John M. Finn
Keyword(s):  
Lie Transforms

scholarly journals Hill Problem Analytical Theory to the Order Four: Application to the Computation of Frozen Orbits around Planetary Satellites

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Martin Lara ◽  
Jesús F. Palacián
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Hill Problem ◽  
Frozen Orbits ◽  
Long Period ◽  
Lie Transforms ◽  
Planetary Satellites ◽  
The Hill ◽  
Order Four

Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that connects the averaged and nonaveraged models. A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.

scholarly journals Lie transforms and motion of a charged particle in a periodic magnetic field

1984 ◽  
Vol 7 (1) ◽  
pp. 159-169
Author(s):  
Sikha Bhattacharyya ◽  
R. K. Roy Choudhury
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Averaging Method ◽  
Second Order ◽  
Lie Series ◽  
Periodic Magnetic Field ◽  
First Order ◽  
Order Solution ◽  
Lie Transforms ◽  
Spatially Periodic

We use the Lie series averaging method to obtain a complete second order solution for motion of a charged particle in a spatially periodic magnetic field. A comparison is made with the first order solution obtained previously by Coffey.

Equivalence for lie transforms

1974 ◽  
Vol 10 (4) ◽  
pp. 497-512 ◽  
Author(s):  
Jacques Henrard ◽  
Jacques Roels
Keyword(s):  
Lie Transforms

The Hamiltonian transformation in quadratic lie transforms

1984 ◽  
Vol 32 (2) ◽  
pp. 99-107 ◽  
Author(s):  
R. A. Howland ◽  
D. L. Richardson
Keyword(s):  
Lie Transforms
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