Chaotic Behavior of the Biharmonic Dynamics System
Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like . The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes under small perturbations. Melnikov method gives analytical criterion for heteroclinic chaos in terms of system parameters. A transition from chaotic to regular motion of the biharmonic oscillator was found as the heteroclinic chaos can be removed by increasing the coefficient of a damping force. The analytical results obtained using Melnikov method have been confirmed by a good match with numeric research.
Features of rotational motion of a spacecraft descending in the Martian atmosphere
Angular motion at atmospheric entry is studied in the paper for a spacecraft with a bi-harmonic moment characteristic. Special attention is given to the case when the spacecraft possesses two stable balanced positions, and, hence, it can oscillate in dense atmospheric layers in the ranges of small or large angles of attack. The averaged equations of spacecraft motion are derived, which allow one to increase the speed of calculations by several orders of magnitude. A real example is presented, which concerns a spacecraft specially designed for descending in the Martian atmosphere.
Researches on Structural Factor Involvement in Oral Tribology
This study is focused on two ceramic materials, D.SING (Ivoclar) and VM13 (emphasis the VITA TN), frequently used in restorative dentistry practice and it comes to complete a full set of results obtained by the authors over several years of research on oral tribology with main influence on oral health. In this way there are involved more specific structural aspects of dental restorative ceramic materials quality as is shown in [1].