Time‐dependent quadratic constants of motion, symmetries, and orbit equations for classical particle dynamical systems with time‐dependent Kepler potentials

1982 ◽  
Vol 23 (4) ◽  
pp. 552-563 ◽  
Author(s):  
Gerald H. Katzin ◽  
Jack Levine
Keyword(s):  
Dynamical Systems ◽  
Time Dependent ◽  
Classical Particle ◽  
Constants Of Motion

FICTON THEORY OF DYNAMICAL SYSTEMS WITH NOISY PARAMETERS

1965 ◽  
Vol 43 (4) ◽  
pp. 619-639 ◽  
Author(s):  
R. C. Bourret
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Dynamical Systems ◽  
Approximate Solutions ◽  
Frequency Parameter ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Graphical Comparison ◽  
The One ◽  
Random Fluctuations

The theory of randomly perturbed waves described previously (Bourret 1962a, b) is presented in a form applicable to purely time-dependent systems, classical or quantum mechanical. It is then applied to the problem of a spin-[Formula: see text] dipole in a magnetic field with random fluctuations. One- and two-ficton processes are taken into account and a "renormalization" approximation is given also. Graphical comparison of the approximate solutions with the exact solution is presented. As a classical example, the harmonic oscillator with a noisy frequency parameter is analyzed in both the one- and two-ficton approximations.

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