• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.389-398
• /
• 2018

In this paper we obtain the condition for the existence of Ricci solitons in nonflat quaternion space form by using Eisenhart problem. Also it is proved that if (g, V, ${\lambda}$) is Ricci soliton then V is solenoidal if and only if it is shrinking, steady and expanding depending upon the sign of scalar curvature. Further it is shown that Ricci soliton in semi-symmetric quaternion space form depends on quaternion sectional curvature c if V is solenoidal.

• Communications of the Korean Mathematical Society
• /
• v.17 no.4
• /
• pp.625-633
• /
• 2002

Recently, Chen establishes sharp relationship between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. In this paper, we establish sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in quaternion projective spaces.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.809-824
• /
• 1997

With the primitive orders in quaternion algebra, theta series associated with these orders are constructed. Here, we studied the space of modular forms generated by these theta series.

• Honam Mathematical Journal
• /
• v.45 no.2
• /
• pp.198-214
• /
• 2023

In the present paper, we investigate homothetic motions determined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable properties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.33 no.11
• /
• pp.48-56
• /
• 2005

Predictive filter theory proposed recently can be characterized by inherent advantages of estimating modelling error and overcoming the disadvantage of the Kalman filter theory. A one-step ahead error is minimized to produce optimized filter performance in the form of the predictive filter. The main advantage of this filter lies in the ability to estimate both state vector and system model error. In this paper, attitude estimation results based upon the predictive filter theory is addressed. Mathematical formulation for estimating bias signal is peformed by using the predictive filter theory, and attitude estimation based upon vector observation is presented. From the results of this study, the potential applicability of the predictive filter is highlighted.

• Advances in aircraft and spacecraft science
• /
• v.5 no.4
• /
• pp.459-475
• /
• 2018

In the field of aerospace engineering, accurate control of a spacecraft's orientation is often very important to mission success. Therefore, attitude control is a technically plentiful and extensively studied subject in controls literature during recent decades. This investigation of spacecraft attitude control is assumed to address two important aspects of the problem solutions. One sliding mode anti-disturbance control for utilization of faulty actuator components and another one disturbance observer based control to improve the pointing accuracy in the absence of anti-vibration equipment for the elastic appendages like a solar panel. Simultaneous occurrence of vibration due to flexible appendages and reaction degradation due to failure in attitude actuators complicates this case. The advantage of this method is acquisition proper control by the combination of disturbance observer and sliding mode compensation that form a fault tolerant control for the concerned satellite attitude control system. Furthermore, the proposed composite method indicates that occurrence the failure in actuators and even elastic solar panel vibration effect may be handled directly without reconfiguring the control components or providing piezoelectric devices. It's noteworthy, attitude quaternion and angular velocity commands are robustly tracked via controllers to become inclined to zero.

• International Journal of Aeronautical and Space Sciences
• /
• v.8 no.1
• /
• pp.10-20
• /
• 2007

For spacecraft attitude control, reaction wheel (RW) steering laws with more than three wheels for three-axis attitude control can be derived by using a control allocation (CA) approach.1-2 The CA technique deals with a problem of distributing a given control demand to available sets of actuators.3-4 There are many references for CA with applications to aerospace systems. For spacecraft, the control torque command for three body-fixed reference frames can be constructed by a combination of multiple wheels, usually four-wheel pyramid sets. Multi-wheel configurations can be exploited to satisfy a body-axis control torque requirement while satisfying objectives such as minimum control energy.1-2 In general, the reaction wheel steering laws determine required torque command for each wheel in the form of matrix pseudo-inverse. In general, the attitude control command is generated in the form of a feedback control. The spacecraft body angular rate measured by gyros is used to estimate angular displacement also.⁵ Combination of the body angular rate and attitude parameters such as quaternion and MRPs(Modified Rodrigues Parameters) is typically used in synthesizing the control command which should be produced by RWs.¹ The attitude sensor signals are usually corrupted by noise; gyros tend to contain errors such as drift and random noise. The attitude determination system can estimate such errors, and provide best true signals for feedback control.⁶ Even if the attitude determination system, for instance, sophisticated algorithm such as the EKF(Extended Kalman Filter) algorithm⁶, can eliminate the errors efficiently, it is quite probable that the control command still contains noise sources. The noise and/or other high frequency components in the control command would cause the wheel speed to change in an undesirable manner. The closed-loop system, governed by the feedback control law, is also directly affected by the noise due to imperfect sensor characteristics. The noise components in the sensor signal should be mitigated so that the control command is isolated from the noise effect. This can be done by adding a filter to the sensor output or preventing rapid change in the control command. Dynamic control allocation(DCA), recently studied by Härkegård, is to distribute the control command in the sense of dynamics⁴: the allocation is made over a certain time interval, not a fixed time instant. The dynamic behavior of the control command is taken into account in the course of distributing the control command. Not only the control command requirement, but also variation of the control command over a sampling interval is included in the performance criterion to be optimized. The result is a control command in the form of a finite difference equation over the given time interval.⁴ It results in a filter dynamics by taking the previous control command into account for the synthesis of current control command. Stability of the proposed dynamic control allocation (CA) approach was proved to ensure the control command is bounded at the steady-state. In this study, we extended the results presented in Ref. 4 by adding a two-step dynamic CA term in deriving the control allocation law. Also, the strict equality constraint, between the virtual and actual control inputs, is relaxed in order to construct control command with a smooth profile. The proposed DCA technique is applied to a spacecraft attitude control problem. The sensor noise and/or irregular signals, which are existent in most of spacecraft attitude sensors, can be handled effectively by the proposed approach.