China
Africa
Explore chapters and articles related to this topic
Motor Vibration and Acoustic Noise
Published in Wei Tong, Mechanical Design and Manufacturing of Electric Motors, 2022
The polar coordinate system uses r as the radial coordinate and ϕ as the angular coordinate. Thus, the Cartesian coordinate system (x, y) can be related to the polar coordinate system (r, ϕ) as x = rcosϕ and y = rsinϕ. Consequently, the equation of the rotating elliptic rotor can be rewritten as res2cos2(ϕ−ωrt)a2+rer2sin2(ϕ−ωrt)b2=1
General Mathematical Functions
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
In traditional mathematics the study of complex numbers leads directly to an alternative plane of trigonometric representation, usually called the polar coordinate system. Conventionally, the polar coordinate system is depicted as based on a point, called the pole, located at the origin of the Cartesian plane, and a ray from this pole, called the polar axis. The polar axis is usually assumed to lie in the positive direction of the x-axis. A point in the polar coordinate system is defined by its directed angle from the polar axis and its directed distance from the pole. Figure 9.4 shows the elements of the polar and Cartesian coordinate systems.
A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates
Published in International Journal of Mathematical Education in Science and Technology, 2020
Vahid Borji, Hedyeh Erfani, Vicenç Font
The polar coordinate system is defined as a two-dimensional coordinate system where each point on the plane has two indicators: a distance from the pole, , as the first coordinate and an angle from a reference direction, , as the second coordinate. In many of undergraduate courses, polar coordinate system is taught with a focus on geometric interpretations, conversions between polar and Cartesian coordinates and sketching polar graphs [1,4].