Mixed forced, parametric, and self-oscillations with nonideal energy source and lagging forces

The purpose of this study is to determine the effect of retarded forces in elasticity and damping on the dynamics of mixed forced, parametric, and self-oscillations in a system with limited excitation. A mechanical frictional self-oscillating system driven by a limited-power engine was used as a model. Methods. In this work, to solve the nonlinear differential equations of motion of the system under consideration, the method of direct linearization is used, which differs from the known methods of nonlinear mechanics in ease of use and very low labor and time costs. This is especially important from the point of view of calculations when designing real devices. Results. The characteristic of the friction force that causes self-oscillations, represented by a general polynomial function, is linearized using the method of direct linearization of nonlinearities. Using the same method, solutions of the differential equations of motion of the system are constructed, equations are obtained for determining the nonstationary values of the amplitude, phase of oscillations and the speed of the energy source. Stationary motions are considered, as well as their stability by means of the Routh–Hurwitz criteria. Performed calculations obtained information about the effect of delays on the dynamics of the system. Conclusion. Calculations have shown that delays shift the amplitude curves to the right and left, up and down on the amplitude–frequency plane, change their shape, and affect the stability of motion.

Geostationary Orbit Transfer with Lunar Gravity Assist from Non-equatorial Launch Site

We show that it is possible to launch a satellite to Geostationary Equatorial orbit (GEO) from the non-equatorial launch site (Naro Space Center in South Korea) even though that is located in the mid-latitudes of the northern hemisphere. When launched from this site, the equatorial inclination after separation will be 80°. We use a lunar gravity assist (LGA) transfer to avoid the excessive ∆V costs of plane change maneuvers. There are eight possible paths for the LGA; there are four paths consisting of Earth departures and free-return types, and there are two nodes of the Moon’s orbit (ascending and descending). We analyze trajectories over five launch periods for each path using a high-fidelity orbit propagation model. We show that the LGA changes the orbital energy of the “cislunar” free-returns more than for the “circumlunar” free-returns, resulting in less geostationary insertion ∆V for the cislunar free-returns. We also show that the geometrical ∆V variation over the different paths is greater than the seasonal ∆V variation. Our results indicate that an ascending departure and cislunar free-return at the descending node have lower ∆V requirements than the other paths, and lower than described in several previous studies.

Twin study—genetic comparison of matrix versus intramatrix rotation in the mandible and three different occlusal planes

Background The purpose of this study is to investigate the heritability of total rotation, matrix rotation, and intramatrix rotation of the mandible in Korean monozygotic (MZ) twins, dizygotic (DZ) twins, and their siblings. Materials and methods The samples consisted of 75 pairs of Korean twins (39.7 + 9.26 years; MZ group, 36 pairs; DZ group, 13 pairs; sibling group, 26 pairs). Lateral cephalograms were taken, and 13 variables related to internal and external mandible rotation were measured. Three types of occlusal planes (bisected occlusal plane, functional occlusal plane, and the MM bisector occlusal plane) were used to evaluate genetic influence on the occlusal plane. Heritability (h2) was calculated by using the intraclass correlation coefficient (ICC) and Falconer’s method. Results With regard to mandibular rotation, the MZ twin group showed significantly higher ICC values compared to the DZ twin and sibling groups. The ICC mean values for 13 cephalometric measurements were 0.85 (MZ), 0.62 (DZ), and 0.52 (siblings) respectively. The heritability of the total rotation (0.48) and matrix rotation (0.5) between the MZ and DZ groups was higher than that of the intramatrix rotation (− 0.14). All of the three types of occlusal plane showed high heritability, and among the three types, the functional occlusal plane showed the highest heritability (h2 = 0.76). Conclusion Based on these findings that showed a strong genetic effect on total rotation and matrix rotation, maintaining these rotations should be carefully considered in the orthodontic treatment plan, while the lower border of the mandible may be responsive to various treatments. Occlusal plane change, especially with regard to the functional occlusal plane, may not be stable due to strong genetic influences.

Application of differential evolution algorithm in the problem of aeroassisted orbital plane change maneuver

The paper deals with application of the differential evolution method in optimizing aeroassisted orbital plane change maneuver performed by an aerospace vehicle with a high lift-to-drag ratio. The vehicle’s motion relative to the Earth is described by a system of differential equations in the flight path axis system. The angle-of-attack and the air path bank angle control programs are presented in the form of Fourier series and thrust control has the form of flip-flop control. The results of solving problems without phase parameter constraints obtained by the differential evolution algorithm were compared with the results obtained using Pontryagin’s maximum principle. The solution of the optimization problem taking into account temperature limitations at the stagnation point was obtained on the basis of the differential evolution algorithm.