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All Journal Jurnal Sains Dasar
Kus Prihantoso Krisnawan
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Identifikasi bifurkasi kodimensi-2 pada sistem flutter dengan menggunakan kriteria Routh Hartono, Hartono; Krisnawan, Kus Prihantoso
Jurnal Sains Dasar Vol 3, No 1 (2014): Jurnal Sain Dasar
Publisher : Universitas Negeri Yogyakarta

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Abstract

In this paper, the codimension-2 bifurcation of a 2-parameter flutter system is identified using Routh’s criterion. Routh’s criterion is a tool to determine the number of roots of a real polynomial in the right half-plane. Based on this criterion, the regions borders of each parameter are determined in order to make the roots of flutter system characteristic equation have negative or positive real parts. A point is taken from each region and the phase portraits of the system are drawn. Based on the Routh’s table and the phase portraits, different dynamical structure that showing a pitchfork-hopf bifurcation is acquired. Key words: pitchfork-hopf bifurcation, flutter system, Routh’s criterion
On the othogonal trajectories and conformal mapping of complex variable functions Krisnawan, Kus Prihantoso; Dhoruri, Atmini
Jurnal Sains Dasar Vol 3, No 2 (2014): Jurnal Sains Dasar
Publisher : Yogyakarta State University

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Abstract

This research goal is to investigate the connection of orthogonal trajectories, analitic functions, and conformal mapping. Orthogonal trajectories are the intersection of two families of mutually perpendicular curves. The analytical property of a complex function f(z) = u + iv is investigated using Cauchy-Riemann conditions and then the geometric shapes of u and v are interpreted. The results showed that if two functions are mutually harmonic conjugate, then they are mutually orthogonal trajectories. If two families of curves of mutually orthogonal trajectories are mapped by conformal mapping then the result functions are also mutually orthogonal trajectories.Key words: orthogonal trajectories, analytic functions, conformal mapping
PARALLEL COORDINATE APPLICATION IN 4 DIMENSION ROOM AT PLANE TRAFFIC DISPLAY Hartono, Hartono; Krisnawan, Kus Prihantoso; Arifah, Husna
Jurnal Sains Dasar Vol 4, No 2 (2015): Jurnal Sains Dasar
Publisher : Yogyakarta State University

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Abstract

This research aims to describe ann-dimensional line on a parallel coordinate and uses the representation as a display of aircraft motion which flies at a straight line and constant velocity. A parallel coordinate of n-dimensional space depicted in the form of nparallel vertical lines which represent axis.Every two adjacent axes have the same distance. A horizontal line that cutsall axes indicates the initial pointsof each axis. In a parallel coordinate,an 15n"> -dimensional point is represented as a polygonal chainwhere the vertices located on its axis. Based on the representations of some of collinear points, a line is described on a parallel coordinate. On the other hand, one can consider a graph of an aircraft motion as a graph of a 4-dimensional space. At a constant speed with a straight line orbit, the graph of an aircraft movementis a graph of 4-dimensional line. The result shows that, on a parallel coordinate, an n-dimensional line represented as 15n-1">  dots. As a consequence, the graph of an aircraft that moveat a constant speed with a straight line orbitrepresented as3 dots. By this representation, the coordinate and altitude of the aircraft can be observes at anytime. It also shows whether the movement of an aircraft disturb (strike or too close to) another plane or not. Keywords: parallel coordinate, n-dimensional space, aircraft movement display