Angular velocity stabilization of underactuated rigid satellites based on energy shaping

Guanjun Chen ◽  
Wei Huo
1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
B. Garfinkel

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

2018 ◽  
Vol 1 (84) ◽  
Vilma Jurevičienė ◽  
Albertas Skurvydas ◽  
Juozas Belickas ◽  
Giedra Bušmanienė ◽  
Dovilė Kielė ◽  

Research  background  and  hypothesis.  Proprioception  is  important  in  the  prevention  of  injuries  as  reduced proprioception  is  one  of  the  factors  contributing  to  injury  in  the  knee  joint,  particularly  the  ACL.  Therefore, proprioception appears not only important for the prevention of ACL injuries, but also for regaining full function after ACL reconstruction.Research aim. The aim of this study was to understand how proprioception is recovered four and five months after anterior cruciate ligament (ACL) reconstruction.Research methods. The study included 15 male subjects (age – 33.7 ± 2.49 years) who had undergone unilateral ACL reconstruction with a semitendinosus/gracilis (STG) graft in Kaunas Clinical Hospital. For proprioceptive assessment, joint position sense (JPS) was measured on both legs using an isokinetic dynamometer (Biodex), at knee flexion of 60° and 70°, and at different knee angular velocities of 2°/s and 10°/s. The patients were assessed preoperatively and after 4 and 5 months, postoperatively.Research results. Our study has shown that the JPS’s (joint position sense) error scores  to a controlled active movement is significantly higher in injured ACL-deficient knee than in the contralateral knee (normal knee) before surgery and after four and five months of rehabilitation.  After 4 and 5 months of rehabilitation we found significantly lower values in injured knees compared to the preoperative data. Our study has shown that in injured knee active angle reproduction errors after 4 and 5 months of rehabilitation were higher compared with the ones of the uninjured knee. Proprioceptive ability on the both legs was  independent of all differences angles for target and starting position for movement. The knee joint position sense on both legs depends upon the rate of two different angular velocities and the mean active angle reproduction errors at the test of angular velocity slow speed was the highest compared with the fast angular velocity. Discussion and conclusions. In conclusion, our study shows that there was improvement in mean JPS 4 and 5 months after ACL reconstruction, but it did not return to normal indices.Keywords: knee joint, joint position sense, angular velocity, starting position for movement.

K. Shibazaki ◽  
H. Nozaki

In this study, in order to improve steering stability during turning, we devised an inner and outer wheel driving force control system that is based on the steering angle and steering angular velocity, and verified its effectiveness via running tests. In the driving force control system based on steering angle, the inner wheel driving force is weakened in proportion to the steering angle during a turn, and the difference in driving force is applied to the inner and outer wheels by strengthening the outer wheel driving force. In the driving force control (based on steering angular velocity), the value obtained by multiplying the driving force constant and the steering angular velocity,  that differentiates the driver steering input during turning output as the driving force of the inner and outer wheels. By controlling the driving force of the inner and outer wheels, it reduces the maximum steering angle by 40 deg and it became possible to improve the cornering marginal performance and improve the steering stability at the J-turn. In the pylon slalom it reduces the maximum steering angle by 45 deg and it became possible to improve the responsiveness of the vehicle. Control by steering angle is effective during steady turning, while control by steering angular velocity is effective during sharp turning. The inner and outer wheel driving force control are expected to further improve steering stability.

2018 ◽  
Vol 49 (1) ◽  
pp. 43-64
Mikhail Alekseyevich Golovkin ◽  
Andrey Aleksandrovich Efremov ◽  
Miroslav Sergeevich Makhnev

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
M.Abdel Wahab

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

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