• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.444-448
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• 2003

In this paper, the Lagrange dynamics is studied. A state space representation of Lagrange dynamics and control algorithm based on the state feedback pole placement are presented. The state space model presented is descriptor type linear parameter dependent system. It is shown that the control algorithms based on the linear system theory can be applicable to the state space representation of Lagrange dynamics. To show that the linear system theory can be applicable to the state space representation of Lagrange dynamics, the LMI based regional pole-placement design algorithm is developed and present two examples.

• Journal of Astronomy and Space Sciences
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• v.38 no.2
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• pp.145-155
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• 2021

In this work, preliminary launch opportunities from NARO Space Center to the Sun-Earth Lagrange point are analyzed. Among five different Sun-Earth Lagrange points, L1 and L2 points are selected as suitable candidates for, respectively, solar and astrophysics missions. With high fidelity dynamics models, the L1 and L2 point targeting problem is formulated regarding the location of NARO Space Center and relevant Target Interface Point (TIP) for each different launch date is derived including launch injection energy per unit mass (C3), Right ascension of the injection orbit Apoapsis Vector (RAV) and Declination of the injection orbit Apoapsis Vector (DAV). Potential launch periods to achieve L1 and L2 transfer trajectory are also investigated regarding coasting characteristics from NARO Space Center. The magnitude of the Lagrange Orbit Insertion (LOI) burn, as well as the Orbit Maintenance (OM) maneuver to maintain more than one year of mission orbit around the Lagrange points, is also derived as an example. Even the current work has been made under many assumptions as there are no specific mission goals currently defined yet, so results from the current work could be a good starting point to extend diversities of future Korean deep-space missions.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.165-171
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• 2014

Let M be a manifold with a volume form ${\omega}$ and $f:M{\rightarrow}M$ be a diffeomorphism of class 𝒞$^1$ that preserves ${\omega}$. We prove that if M is almost bounded for the diffeomorphism f, then M is chain recurrent. Moreover, we get that Lagrange stable volume-preserving manifolds are also chain recurrent.

• Journal of Advanced Marine Engineering and Technology
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• v.27 no.7
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• pp.862-871
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• 2003

In this paper, we addressed a modeling for the magnetic levitation stage. This planar magnetic levitator employs four permanent magnet liner motors. Each motor generates vertical force for suspension against gravity, as well as horizontal force for propulsion. Therefore. this stage can generate six degrees of freedom motion by the combination of forces. We derived a mechanical dynamics equation using Lagrangian method and electromechanical dynamics equation by using Co-energy method. Based on the derived dynamics, we can analyze the stage motion that is subject to the input currents and forces.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.674-679
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• 2005

This paper is concerned with the application of perturbation method to the dynamic analysis of space structure floating in space. In dealing with the dynamics of space structure, the use of Lagrange's equations of motion in terms of quasi-coordinates were suggested to derive hybrid equations of motion for rigid-body translations and elastic vibrations. The perturbation method is then applied to the hybrid equations of motion along with discretization by means of admissible functions. This process is very tiresome. Recently, a new approach that applies the perturbation method to the Lagrange's equations directly was proposed and applied to the two-dimensional floating structure. In this paper, we propose the application of the perturbation method to the Lagrange's equations of motion in terms of quasi-coordinates. Theoretical derivations show the efficacy of the proposed method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.9 s.102
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• pp.1030-1036
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• 2005

This paper is concerned with the application of perturbation method to the dynamic analysis of space structure floating in space. In dealing with the dynamics of space structure, the use of Lagrange's equations of motion in terms of quasi-coordinates were suggested to derive hybrid equations of motion for rigid-body translations and elastic vibrations. The perturbation method is then applied to the hybrid equations of motion along with discretization by means of admissible functions. This process is very tiresome. Recently, a new approach that applies the perturbation method to the Lagrange's equations directly was proposed and applied to the two-dimensional floating structure. In this paper. we propose the application of the perturbation method to the Lagrange's equations of motion in terms of quasi-coordinates. Theoretical derivations show the efficacy of the proposed method.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.141-154
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• 2024

This article offers a thorough exploration of a modified Black-Scholes model featuring two assets. The determination of option prices is accomplished through the Black-Scholes partial differential equation, leveraging the variational iteration method. This approach represents a semi-analytical technique that incorporates the use of Lagrange multipliers. The Lagrange multiplier emerges as a beacon of efficiency, adeptly streamlining the computational intricacies, and elevating the model's efficacy to unprecedented heights. For better understanding of the presented system, a graphical and tabular interpretation is presented with the help of Maple software.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.35-43
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• 1996

A computer program for automatic deriving the symbolic equations of motion for robots using the programming language MATHEMATICA has been developed. The program, developed based on the Lagrange formalism, is applicable to the closed chain robots as well as the open chain robots. The closed chains are virtually cut open, and the kinematics and dynamics of the virtual open chain robot are analyzed. The constraints are applied to the virtually cut joints. As a result, the spatial closed chain robot can be considered as a tree structured open chain robot with kinematic constraints. The topology of tree structured open chain robot is described by a FATHER array. The FATHER array of a link indicates the link that is connected in the direction of base link. The constraints are represented by Lagrange multipliers. The parallel robot, DELTA, having three-dimensional closed chains is modeled and simulated to illustrate the approach.

• Journal of Astronomy and Space Sciences
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• v.31 no.1
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• pp.91-99
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• 2014

The atmospheric flow in the 3-Cell model of global atmosphere circulation is described by the Lagrange's equation of the non-inertial frame where pressure force, frictional force and fictitious force are mixed in complex form. The Coriolis force is an important factor which requires calculation of fictitious force effects on atmospheric flow viewed from the rotating Earth. We make new Mathematica platform to solve Lagrange's equation by numerical analysis in order to analyze dynamics of atmospheric general circulation in the non-inertial frame. It can simulate atmospheric circulation process anywhere on the earth. It is expected that this pedagogical platform can be utilized to help students studying the atmospheric flow understand the mechanisms of atmospheric global circulation.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.5
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• pp.128-137
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• 1998

A numerical approach for performing kinematic design sensitivity analysis of vehicle suspension systems is presented. Compared with the conventional analytical methods, which require explicit derivation of sensitivity equations, the proposed numerical method can be applied to any type of suspension systems without obtaining sensitivity equations, once any kinematic analysis procedure is established. To obtain sensitivity equations, a numerical differentiation algorithm that uses the third order Lagrange polynomial is developed. The algorithm efficiently and accurately computes the sensitivity of various vehicle static design factors with respect to kinematic design variables. Through a suspension design problem, the validity and usefulness of the method is demonstrated.