• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.559-567
• /
• 2015

This paper gives the expression of dual quaternions and provides differential operators in dual quaternions. The paper also represents the derivative of dual quaternion-valued functions by using a corresponding Cauchy-Riemann system in dual quaternions.

• Honam Mathematical Journal
• /
• v.38 no.4
• /
• pp.675-683
• /
• 2016

We give the representation of Fibonacci quaternions for convenient calculus. We research the corresponding properties of Fibonacci quaternions and some examples of a function with values in modified Fibonacci quaternions.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.187-187
• /
• 2000

This paper presents the comparison of Euler-Rodrigues quaternion and Euler Angles using attitude kinematics for aircraft flight simulation. It is hard for PC-Level to accomplish real-time simulation. The purpose of this paper is to accomplish real-time simulation of the aircraft dynamics modeling parts and the graphics parts. The computation time is more reduced in case of applying quaternions than Euler Angles. This paper provides a quaternions algorithm and it's applications for the real-time simulation.

• The Pure and Applied Mathematics
• /
• v.22 no.1
• /
• pp.65-74
• /
• 2015

In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.

• East Asian mathematical journal
• /
• v.31 no.5
• /
• pp.653-658
• /
• 2015

In this paper, we consider split quaternionic functions defined on an open set of split quaternions and give the split quaternionic functions whose each inverse function is sp-hyperholomorphic almost everywhere on ${\Omega}$. Also, we describe the definitions and notions of pseudoholomorphic functions for split quaternions.

• 제어로봇시스템학회:학술대회논문집
• /
• 1995.10a
• /
• pp.115-118
• /
• 1995

This paper present an attitude control using quaternions as feedback attitude errors. The Euler's eigenaxis rotation provides the shortest angular path between two attitudes. This eigenaxis rotation can be achieved by using quaternions since quaternions are related with the eigenaxis. The suggested controller uses error quaternions and body angular rates and generates a decoupling control torque that counteracts the natural gyroscopic coupling torque. The momentum dumping strategy using the earth magnetic field is also applied in this paper to unload the angular momentum of the reaction wheels used in the attitude control.

• East Asian mathematical journal
• /
• v.31 no.1
• /
• pp.127-134
• /
• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.97-104
• /
• 2016

We give representations of differential operators and rules for addition and multiplication of dual quaternions. Also, we research the notions and properties of a regular function and a corresponding harmonic function with values in dual quaternions of Clifford analysis.

• International Journal of Precision Engineering and Manufacturing
• /
• v.8 no.4
• /
• pp.16-21
• /
• 2007

Robotic applications, such as automatic fish cutting, require online trajectory planning because the material properties of the object, such as the bone or flesh conditions, are not known in advance. Different trajectories are required when the material properties vary. An effective online trajectory-planning algorithm is proposed using quaternions to determine the position and orientation of a robot manipulator with a spherical wrist. Quaternions are free of representation singularities and permit computationally efficient orientation interpolations. To prevent singular configurations, the exact locations of the kinematic singularities of the PUMA 560 manipulator are derived and geometrically illustrated when a forearm offset exists and the third link length is not zero.

• East Asian mathematical journal
• /
• v.31 no.5
• /
• pp.667-675
• /
• 2015

In this paper, we provide some properties of several left regular functions in Clifford analysis. We find the corresponding Cauchy-Riemann system and conjugate harmonic functions of the harmonic functions, for each left regular function in the sense of several complex variables. And we investigate certain properties of generalized quaternions in Clifford analysis.