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All Journal Jurnal Sains Dasar
Husna Arifah, Husna
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THE EFFECT OF NONLINEAR DAMPING TO A DYNAMICAL SYSTEM WITH CENTER PHASE PORTAIT

Jurnal Sains Dasar Vol 4, No 1 (2015): Jurnal Sains Dasar
Publisher : Yogyakarta State University

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Abstract

This paper discusses the effect of nonlinear damping to a 2-dimesional system that has center phase portrait. The phase portraits of the damped system are drawn for 3 different values of parameter. These phase portraits stand as the numerical proof of phase portrait change. To prove the change analiticaly, we use the theorem that guarantee the existence of periodic solution. The result shows that nonlinear damping changes the phase portrait topologically. It means that the system undergoes a generalized Hopf bifurcation. Keywords: generalized Hopf bifurcation, center phase portrait, periodic solution

PARALLEL COORDINATE APPLICATION IN 4 DIMENSION ROOM AT PLANE TRAFFIC DISPLAY

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