Weakly nonlinear oscillatory problems in engineering dynamics are frequently presented by nonlinear ordinary differential equations. Very few of such equations have exact solutions, thus the need for approximation techniques. In this study, the classical perturbation method, namely the Lindstedt-Poincare method (L-P method) is discussed. In most work, the L-P method is used to obtain uniformly ...

We present a review of our previous ab initio calculations of Stark broadening parameters using semi-classical perturbation method for the calculation of Stark widths and shifts, and the SUPERSTRUCURE (SST) code for the determination of atomic structure. SST code takes into account the configuration interactions and relativistic effects. New results are also presented for some spectral lines of...

EXAFS (extended X-ray absorption fine structure) investigations are reported concerning the thermal expansion behaviour of silver in an extended range of temperature from 10 K to about 950 K measured in transmission mode. Both the ratio method and an EXAFS fitting procedure were applied to reveal the temperature dependence of EXAFS parameters. Models based on quantum and classical thermodynamic...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

In the presence of nonvanishing perturbations, it is often the case that asymptotic stability is not possible and hence the trajectories of a system can only be guaranteed to be uniformly ultimately bounded. This paper presents a method for estimating ultimate bounds in both continuousand discrete-time systems. The method is introduced for linear systems and is then applied to nonlinear systems...

After brief personal recollections of the author’s long-time friendship with Misha Marinov the problem of particle production by classical timevarying scalar field is discussed. In the quasiclassical limit the calculations are done by imaginary time method developed, in particular, in Marinov’s works. The method permits to obtain simple analytical expressions which well agree with the later fou...

Classical hamiltonian perturbation theory formulated in terms of action-angle variables is applied to develop a general and systematic method for calculating the influence of anharmonic perturbations on the motion of a charged particle in a Penning trap. Action-angle variables are ideally suited to determine the shifts of the characteristic frequencies in a perturbed orbit. The application of t...