One form of the differential equations for the elements of a hyperbolic orbit
One form of the differential equations for the elements of a hyperbolic orbit
V.M. Chepurova
Differential equations are derived in a very general form for the elements of a hyperbolic orbit which is an intermediate orbit for a point mass moving in the gravitational field of a compact planet. The orbit is constructed on the basis of a symmetric version of the problem of two fixed centers. The only information available about the perturbing function of these equations is that it is of a gravitational nature.
Show AbstractParametric frequency dividers with an abrupt nonlinearity
Parametric frequency dividers with an abrupt nonlinearity
A.N. Lagutkin
Synchronous oscillation of parametric generators is analyzed on the basis of the method of slowly varying amplitudes for the case in which the nonlinear element is turned on repeatedly over a period of the subharmonic oscillations. When the nonlinear element is turned on repeatedly, the bands of Internal self-synchronization and division decrease with increasing value of n, the self-synchronization order, more rapidly (~ 1/n^3/^2), than In the case in which the nonlinear element is turned on only once (~l/n). The decrease is nevertheless weaker than the decrease in the bands upon the formation of combination frequencies at a gradual nonlinearity.
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