The flexible joint robot manipulators provide various benefits, but also present many control challenges such as nonlinearities, strong coupling, vibration, etc. This paper proposes optimal second order integral sliding mode control (OSOISMC) for a single link flexible joint manipulator to achieve robust and smooth performance. Firstly, the integral sliding mode control is designed, which consists of a linear quadratic regulator (LQR) as a nominal control, and switching control. This control guarantees the system robustness for the entire process. Then, a nonsingularterminal sliding surface is added to give a second order integral sliding mode control (SOISMC), which reduces chartering effect and gives the finite time convergence as well. S

Acquires this research importance of addressing the subject (environmental
problems) with age group task, a category that children pre-school, and also
reflected the importance of research, because the (environmental problems)
constitute a major threat to the continuation of human life, particularly the
children, so the environment is Bmchkladtha within kindergarten programs
represent the basis of a hub of learning where the axis, where the kindergarten took
into account included in the programs in order to help the development of
environmental awareness among children and get them used to the sound practices
and behaviors since childhood .
From the foregoing I felt the researcher that the phenomenon of (enviro

In this study, the modified Rayleigh-Ritz method and Fourier series are used to determine the thermal buckling behavior of laminated composite thin plates with a general elastic boundary condition applied to in-plane uniform temperature distribution depending upon classical laminated plate theory(CLPT). A generalized procedure solution is developed for the Rayleigh-Ritz method combined with the synthetic spring technique. The transverse displacement of the orthotropic rectangular plates is not a different term as a new shape expansion of trigonometric series. In this solution approach, the plate transverse deflection and rotation due to bending are developed into principle Fourier series with a sufficient smoothness auxi

The ground-state properties of exotic ¹⁸N and ²⁰F nuclei, including the neutron, proton and matter densities and related  radii are investigated using the two-body model of   within Gaussian (GS) and Woods Saxon (WS) wave functions. The long tail is evident in the computed neutron and matter densities of these nuclei. The plane wave Born approximation (PWBA) is  calculate the elastic form factors of these exotic nuclei. The variation in the proton density distributions due to the presence of the extra neutrons in ¹⁸N and ²⁰F leads to a major difference between the elastic form factors of these exotic nuclei and their stable isotopes ¹⁴N and ¹⁹F. The reaction c

In this investigation, Rayleigh–Ritz method is used to calculate the natural frequencies of rectangular isotropic and laminated symmetric and anti-symmetric cross and angle ply composite plate with general elastic supports along its edges. Each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so-called residual displacement function at the edges. Perhaps more importantly, this study has developed a general approach for deriving a complete set of admissible functions that can be applied to various boundary conditions. Several numerical examples are studied to demonstrate the accuracy and convergence of the current s

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl