In literature, three-dimensional (3D) consolidation equation by exists in polar coordinates only that means for combined vertical and radial consolidation. A principle of super position of rate of settlement for 2D and 3D consolidations is introduced. Using this principle, Carillos equation is ...
Both a point [xyz] T and a line [ABC] T are represented by triplets, and they can be interchanged in the homogeneous equation of a line. This concept can be generalised and points are indistinguishable to planes for the 3D projective space. This symmetry is known as the duality of...
1.The measurement equation is built in theline-of-sight Cartesian coordinate system(LCCS) in the paper.提出了在视线坐标系中建立观测方程,将笛卡尔坐标系中的目标运动方程转换到视线坐标系中,使得雷达观测量尤其是多普勒速度观测与目标状态呈线性关系,并推导得到了该坐标系下的卡尔曼滤波算法,比较了与标准卡尔曼...
r2= ratio of the distance between P2to P - to the distance of P1to P2 For the midpoint between P1and P2: - and eq. 2 and 3 can be expressed as Example - Midpoint on Line The midpoint on the line in the example above can be calculated as ...
The relative root mean squared error (RRMSE) for T1, T2 and T1ρ, and the mean RRMSE of the three parameters were computed to evaluate the performance of FB-MultiMap with different flip angle combinations in simulation and phantom studies. The calculation equation of RRMSE is provided in the ...
This quadratic form can be interpreted as an equation of an ellipsoid, called a confidence region in statistics or an error ellipsoid in geodetic practice. The understanding is that if we know the covariance matrix C and select a probability level α we are comfortable with, then the vector ...
Let's look at the open field line, Φ component is zero, the field line equation is: d r B r = r d θ B θ , since the field components are radius-angle separatable, the equation can be convert to: 125 / ( 8 r 2 ) − r 125 / ( 4 r 3 ) + 1 d r = cos (...
From the latter equation, it straightforwardly follows that the eigenvalues of LGH are of the form (3) ΛGαβH = ΛGα + ΛβH ∀ α = 1, … nG and β = 1, … nH , (4) that is the eigenvalues of the Laplacian matrix associated to the Cartesian product are ...
They are simply calculated from the incremental changes in the body frame given by the dead-reckoning system. Equation (3.4.4) is a simple forward difference representation of the partial differential equation which relates the Euler angle to the body rates. It is acceptable if Δψc is small...
The problem of the transformation is reduced to solving the equation 2 sin (psi-Omega)=c sin 2 psi, where Omega=arctg[bz/(ar)], c=(a 2-b 2)/[(ar) 2+(bz) 2]... KM Borkowski - 《Bulletin Geodesique》 被引量: 122发表: 1989年 Ordering the Earth's magnetic field by geocentric...