We present a version of Opial’s inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.

The simulation of the store separation using the automatic coupling of dynamic equations with flow aerodynamics is addressed. The precision and cost (calculation time) were considered as comparators. The method used in the present research decreased the calculation cost while limiting the solution error within a specific and tolerable interval. The methods applied to model the aerodynamic force...

The theory of impulsive differential equations is emerging as an important area of investigation, since it is a lot richer than the corresponding theory of differential equations without impulse effects. Moreover, such equations may exhibit several real world phenomena in physics, biology, engineering, etc. (see [3, 4, 20]). At the same time, the boundary value problems for impulsive differenti...

starting from two-dimensional (2d) equations of motion, discretized formulations for transient behavior of soil-structure interaction problems have been derived. two different dynamic infinite elements taking into account single and two-wave types are presented in transformed space. by coupling the infinite elements with standard finite elements, an ordinary finite element procedure is used for...

The unification and extension of continuous calculus, discrete calculus, q-calculus, and indeed arbitrary real-number calculus to time-scale calculus, where a time scale is simply any nonempty closed set of real numbers, were first accomplished by Hilger in [4]. Since then, time-scale calculus has made steady inroads in explaining the interconnections that exist among the various calculuses, an...

This study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. Linearization assumptions which have already been used by Hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...