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An accelerometer was announced that used infrared light to measure the change in distance between two micromirrors in a Fabry–Perot cavity. The proof mass is a single silicon crystal with a mass of 10–20 mg, suspended from the first mirror using flexible 1.5 μm-thick silicon nitride (Si 3 N 4) beams. The suspension allows the proof mass to ...
An inertial navigation system (INS; also inertial guidance system, inertial instrument) is a navigation device that uses motion sensors (accelerometers), rotation sensors and a computer to continuously calculate by dead reckoning the position, the orientation, and the velocity (direction and speed of movement) of a moving object without the ...
The probabilist's Hermite polynomials defined above are orthogonal with respect to the standard normal probability distribution, whose density function is , which has expected value 0 and variance 1. Scaling, one may analogously speak of generalized Hermite polynomials [ 13 ] He n [ α ] ( x ) {\displaystyle \operatorname {He} _{n}^{[\alpha ...
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
However, normal may also refer to the magnitude of a vector. In particular, a set is called orthonormal (orthogonal plus normal) if it is an orthogonal set of unit vectors. As a result, use of the term normal to mean "orthogonal" is often avoided. The word "normal" also has a different meaning in probability and statistics.
Let stand for ,, or . The Stiefel manifold () can be thought of as a set of n × k matrices by writing a k-frame as a matrix of k column vectors in . The orthonormality condition is expressed by A*A = where A* denotes the conjugate transpose of A and denotes the k × k identity matrix.
In the theory of orthogonal functions, Lauricella's theorem provides a condition for checking the closure of a set of orthogonal functions, namely: . Theorem – A necessary and sufficient condition that a normal orthogonal set {} be closed is that the formal series for each function of a known closed normal orthogonal set {} in terms of {} converge in the mean to that function.
Accelerometers (in their simplest terms) measure the distortion of a spring. Inertial accelerations are ones that (in the limit case of a small accelerometer, which normal accelerometers approximate quite well in fact) affect every part of an object the same, and hence they can cause no distortion of the spring, and they read zero; e.g. freefall.
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