SMITH-TYPE STABILITY THEOREMS FOR THE DAMPED LINEAR OSCILLATOR
نویسندگان
چکیده
منابع مشابه
Linear Fractionally Damped Oscillator
The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...
متن کاملThe Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters
and Applied Analysis 3 where a t , b t satisfy A and c t is a continuous, T -periodic functions, n ≥ 2, e : R × B 0 → R is a continuous function with continuous derivatives of all orders with respect to the second variable, T -periodic in t, and e t, x O ( |x| ) , x −→ 0, uniformly with respect to t ∈ R. 1.9 It is well-known that 1.8 can be unstable when linear oscillator 1.1 is stable. For the...
متن کاملThe Nonlinearly Damped Oscillator
We study the large-time behaviour of the nonlinear oscillator mx′′ + f(x′) + k x = 0 , where m, k > 0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f(x′) = A |x′|α−1x′ with α real, A > 0. We characterize the existence and behaviour of fast orbits, i....
متن کاملCOMPARING NUMERICAL METHODS FOR THE SOLUTION OF THE DAMPED FORCED OSCILLATOR PROBLEM
In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.
متن کاملQuantizing the damped harmonic oscillator
We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigrou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Dynamic Systems and Applications
سال: 2018
ISSN: 1056-2176
DOI: 10.12732/dsa.v27i2.6