• Journal for History of Mathematics
• /
• v.29 no.4
• /
• pp.243-254
• /
• 2016

This research identifies the elements of the methodologies of Newton's discovery of his dynamics. These methodologies involve the transformation of preceding theoretical concepts and the discovery of common cause. This essay consists of two parts within historical case studies of Newton's works. The elements of the method of discovery consists of the transformation of preceding concepts and the identification of common cause in the formation of the research program's hard cores and protective belts. Newton transformed their predecessors' concepts to find out appropriate common causes in his dynamical theory. The transformed theoretical concepts are synthesized to be constructed as the elements of common cause which provide the foundations of Newtonian research programs.

• Journal of Korean Philosophical Society
• /
• v.148
• /
• pp.157-181
• /
• 2018

The aim of this essay is to identify elements of methodologies to investigate the development of Newtonian dynamics. This methodology involves the transformation and synthesis of preceding theories. My essay attempts to confirm my assertion by analyzing historical case of Newton's discovery of his dynamics. While discovering his mechanistic theory, Newton reconstructed theoretical concepts and structures of intellectual predecessors, such as Aristotle, Descartes, Galileo, and Kepler. Newton's synthesis was possible only after carefully reconstructing the appropriate and useful ideas of previous natural philosophers' ideas. As a result, Newtonian dynamics are completed with these modified and integrated concepts incorporated into Newton's law of motion and space-time concepts. This study consists of two parts. First, Lakatos' research program has been applied in order to analyze the structure of Newtonian dynamics. Second, the aforementioned methodologies of discovery are distilled from the case study.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.8 no.6
• /
• pp.584-590
• /
• 1984

This study is to develop a program, with which the motion of the system can be simulated in view of kinematics and dynamics, and then evaluate functional capabilities of many robots in order to select the most suitable one for any given working conditions. According to the theory of Denavit & Hartenberg, rectangular coordinate is set at each joint in the robot of six joints, as this one is the major concern, and transformation matrices are derived between any two coordinates. The necessary displacement of each joint for executing a given a work is obtained from the position and posture transformation and the in-stantaneous velocity of the joint is got from given velocity distribution of the path. The necessary torque of each joint is finally calculated by Newton-Euler Method. This simulation program is applied to a robot with six rotational joints, Rotational angle and torque to time which has a given motion trajectory are figured and also torque to r.p.m.

• Communications of Mathematical Education
• /
• v.36 no.1
• /
• pp.23-38
• /
• 2022

The study provided a perspective on which readers can see Newton's proof heuristically in order to overcome the difficulty of proof showing 'QT²/QR converges to the latus rectum of ellipse' in the proof of the inverse square law of Newton's Principia. The heuristic perspective is as follows: The starting point of the proof is the belief that if we transform the denominators and numerators of QT²/QR into expression with respect to segments related to diameter and conjugate diameter, we may obtain some constant, the desired value, by their relationship PV × VG/QV² = PC²/CD² in Apollonius' Conic sections. The heuristic perspective proposed in this study is meaningful because it can help readers understand Newton's proof more easily by presenting the direction of transformation of QT²/QR.

• The Journal of the Acoustical Society of Korea
• /
• v.22 no.8
• /
• pp.660-669
• /
• 2003

This paper describes a theory to calculate sound source field from the spatial transform of sound field and the measured cross-power spectrum of sound pressure over a hologram plane close to a sound source, Calculating method is proposed to solve sound pressures from cross-power spectrums over a hologram plane, For this, Taylor series for the nonlinear equations is expanded, and it is calculated using Newton-Raphon method, Also, a wave number filter is used to reduce errors that is occurred on the backward propagation, and is performed numerical simulation of the circular piston sound source with infinite baffle in water to verify the proposed theory.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.17 no.3
• /
• pp.257-264
• /
• 1999

The lens distortions were corrected directly using the high-order polynomial which was offered in camera calibration data for the forward transformation and the root of Newton-Raphson's $2\times{2}$ nonlinear system for the backward transformation. The 0.04~0.08 pixels increase in accuracy was indicated through the use of direct correction of lens distortions instead of least square methods of commercial software. The least square adjustment method of high-order polynomial requires many control points which has a same weight. But this suggested method which is unnecessary to determine control points was developed and applied. The algorithm showed improved efficacy.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.55 no.4
• /
• pp.147-153
• /
• 2006

In this paper, we propose a new delay-dependent criterion on the robust stability of time-delayed linear systems having norm bounded uncertainties. Based on new form of Lyapunov-Krasovskii functional and the Newton-Leibniz formula, we drive a result in the form of LMI which guarantees the robust stability without any model transformation. The Newton-Leibniz equation was used to relate the cross terms with free matrices. Finally, we show the usefulness of our result by two numerical examples.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.725-743
• /
• 2017

We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.

• Structural Engineering and Mechanics
• /
• v.3 no.3
• /
• pp.245-253
• /
• 1995

A combination of Riccati transfer matrix method and finite element method is proposed for obtaining vibration frequencies of structures. This method reduces the propagation of round-off errors produced in the standard transfer matrix method and finds out the values of the frequency by Newton-Raphson method. By this technique, the number of nodes required in the regular finite element method is reduced and therefore a microcomputer may be used. Besides, no plotting of the value of the determinant versus assumed frequency is necessary. As the application of this method, some numerical examples are presented to demonstrate the accuracy as well as the capability of the proposed method for the vibration of structures.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10a
• /
• pp.926-930
• /
• 1993

An efficient method of formulating the equations of motion of multibody systems is presented. The equations of motion for each body are formulated by using Newton-Eulerian approach in their generic form. And then a transformation matrix which relates the global coordinates and relative coordinates is introduced to rewrite the equations of motion in terms of relative coordinates. When appropriate set of kinematic constraints equations in terms of relative coordinates is provided, the resulting differential and algebraic equations are obtained in a suitable form for computer implementation. The system geometry or topology is effectively described by using the path matrix and reference body operator.