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The examples in this article apply to active rotations of vectors counterclockwise in a right-handed coordinate system (y counterclockwise from x) by pre-multiplication (R on the left). If any one of these is changed (such as rotating axes instead of vectors, a passive transformation ), then the inverse of the example matrix should be used ...
For example, to study the equations of ellipses and hyperbolas, the foci are usually located on one of the axes and are situated symmetrically with respect to the origin. If the curve (hyperbola, parabola , ellipse, etc.) is not situated conveniently with respect to the axes, the coordinate system should be changed to place the curve at a ...
Top: Output signal as a function of time. Middle: Input signal as a function of time. Bottom: Resulting Lissajous curve when output is plotted as a function of the input. In this particular example, because the output is 90 degrees out of phase from the input, the Lissajous curve is a circle, and is rotating counterclockwise.
1.1 Rotation matrix: counterclockwise vs. clockwise. 3 comments. 1.2 Convert procedure to formula? 5 comments. 1.3 Another number theory problem. 7 comments. 1.4 Name ...
For example, if the object first circles the origin four times counterclockwise, and then circles the origin once clockwise, then the total winding number of the curve is three. Using this scheme, a curve that does not travel around the origin at all has winding number zero, while a curve that travels clockwise around the origin has negative ...
Dextrorotation and laevorotation (also spelled levorotation) [1] [2] in chemistry and physics are the optical rotation of plane-polarized light.From the point of view of the observer, dextrorotation refers to clockwise or right-handed rotation, and laevorotation refers to counterclockwise or left-handed rotation.
Graphs of roses are composed of petals.A petal is the shape formed by the graph of a half-cycle of the sinusoid that specifies the rose. (A cycle is a portion of a sinusoid that is one period T = 2π / k long and consists of a positive half-cycle, the continuous set of points where r ≥ 0 and is T / 2 = π / k long, and a negative half-cycle is the other half where r ...
An object with an axial tilt up to 90 degrees is rotating in the same direction as its primary. An object with an axial tilt of exactly 90 degrees, has a perpendicular rotation that is neither prograde nor retrograde. An object with an axial tilt between 90 degrees and 180 degrees is rotating in the opposite direction to its orbital direction.