New canonical perturbation method for complete set of integrals of motion

1969 ◽  
Vol 19 (1) ◽  
pp. 130-133 ◽  
Author(s):  
J. Lacina
Keyword(s):  
Perturbation Method ◽  
Integrals Of Motion ◽  
Canonical Perturbation ◽  
Complete Set

Nonlinear Resonances in a Column Subjected to a Constant End Force

1980 ◽  
Vol 47 (2) ◽  
pp. 409-414 ◽  
Author(s):  
M. R. M. Crespo da Silva
Keyword(s):  
Perturbation Method ◽  
Analytical Determination ◽  
Free Oscillations ◽  
Integrals Of Motion ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Nonlinear Resonances ◽  
Canonical Perturbation

A canonical perturbation method based on Hamilton-Jacobi theory, used together with Galerkin’s method, is employed to analyze the nonlinearly coupled transverse free oscillations of columns subjected to a constant end force. Integrals of motion, readily obtained from this type of analysis, are used to allow the analytical determination of the main characteristics of the resonant motion and of the region of resonance of the system.

scholarly journals New Approach to the Planetary Theory

1979 ◽  
Vol 81 ◽  
pp. 69-72 ◽  
Author(s):  
Manabu Yuasa ◽  
Gen'ichiro Hori
Keyword(s):  
Perturbation Method ◽  
Canonical Form ◽  
Equations Of Motion ◽  
Disturbing Function ◽  
Averaging Principle ◽  
The Sun ◽  
Planetary Theory ◽  
New Approach ◽  
Canonical Perturbation ◽  
Relative Coordinates

A new approach to the planetary theory is examined under the following procedure: 1) we use a canonical perturbation method based on the averaging principle; 2) we adopt Charlier's canonical relative coordinates fixed to the Sun, and the equations of motion of planets can be written in the canonical form; 3) we adopt some devices concerning the development of the disturbing function. Our development can be applied formally in the case of nearly intersecting orbits as the Neptune-Pluto system. Procedure 1) has been adopted by Message (1976).

An extended canonical perturbation method

1973 ◽  
Vol 7 (1) ◽  
pp. 77-90 ◽  
Author(s):  
J. S. Choi ◽  
B. D. Tapley
Keyword(s):  
Perturbation Method ◽  
Canonical Perturbation
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