当p=\pm90^{\circ}\时,\cos p=0\,除数为0会导致公式失效。前面我们也知道,pitch旋转90度时会导致万向锁Gimbal lock。这种情况下,我们认为bank=0,且已知\cos p=0\。再代回原矩阵公式中可得 \begin{aligned} & {\left[\begin{array}{ccc} \cos h \cos b+\sin h \sin p \sin b & \sin b \...
Arrangement for converting the angular position of a transducer axis in one of the angle function values sin and / or cos digital code formedLENZ DR-ING KARL LUDWIG
The unit circle is is a circle with a radius of one and is broken down using two special right triangles. It is useful in mathematics for many reasons, most specifically helping with solving trigonometric functions such as sine, cosine, and tangent. This lesson is going to review the unit ...
The image above shows the distance between two stations, displaying both thedirect distance(roughly 570.14m or 0.354 mi) andnavigatable distance(0.5mi). Considering it would be impossible to navigate your bicycle through buildings, the practical route along navigatable roads is longer. Even if...
The 0.5% quote is for error in the great-circle distance between two points so not strictly relevant to this question. I would think when converting lat-long to Cartesian coordinates with the origin at the centre of the earth, the errors from assuming a spherical earth could be significant....
asked 5 years, 5 months ago modified 4 years, 4 months ago viewed 1k times 1 i am using quaternions to describe 3d rotations which parametrized by euler angles, and as a preliminary task i am trying to implement conversion routines that go between euler angles and quaternions. using the ...
The integral above is a hopeless mess as it is. But if we convert it into polar coordinates, we will find that it is most readily handled. To make the conversion, we will need to use the familiar relations between Cartesian and polar variables: ...
Since the average value of the varying radius r when θ=0 and when θ=π is the major axis and since r×sinθ when θ=cos-1(1/n) is the minor axis, the major axis, the minor axis, and the elliptic rate of the elliptic cylinder surface are expressed by Equations (14)-(16), re...
The video signal is next filtered by a high-pass filter 36 which will typically be of the Hilbert type referred to above. Thus, as mentioned above, a filter of the Hilbert type has the effect of differentiating the signal, hence providing a clear distinction between positive and negative obje...
Am I doing something incorrect or there is some math behind it I am not seeing (and maybe ask this on Mathoverflow boards?).UPDATEIt is not necessary to cross boards, as someone correctly pointed this conversion is not meaningful for computing the exact distance between two points (the distan...