the study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. a number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. the main objectives of this review are: 1) to outline the characteristic features of...

In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and...

This paper considers a class of switched dynamical systems to which two periodic inputs are applicable. We derive a one-dimensional (1-D) return map and its derivative analytically for arbitrary shapes of the inputs. Based on the derivative, we introduce a slope chart that displays the relationship between the slope of the return map and that of the inputs. Applying the slope chart to a simplif...

In 1934 Biemond and Daniels first showed that the serum potassium level fell during paralytic episodes in patients with familial periodic paralysis. Subsequently a normokalaemic form of the disease was recognized (1951), while more recently a hyperkalaemic variety was described by Helweg-Larsen, Hauge, and Sagild (1955). This last type of periodic paralysis was given the name adynamia episodica...

Typically, many of the modern buildings have concrete walls constructed from cinder block walls, that have periodic nature in their relative dielectric constant. This periodic nature excites higher-order Floquet harmonic modes at microwave frequencies, which leads to the propagation of scattered waves along with non-specular directions. Periodic structures exhibit different behaviors when illum...

Moiré phenomena of different types are frequently encountered in electronic imaging. Most common are moiré effects that occur between periodic structures. These effects have been intensively investigated in the past, and their mathematical theory is today fully understood. The same is true for moiré effects between repetitive layers (i.e., between geometric transformations of periodic layers). ...