Admittance matrix

Laplacian matrix (L) ( admittance matrix, Kirchhoff matrix)... 

Laplacian matrix (L) (= admittance matrix, Kirchhoffmatrix, combinatorial Laplacian matrix) This is a square Ax A symmetric matrix, A being the number of vertices in the molecular graph, obtained as the difference between the vertex degree matrix V and the adjacency matrix A [Mohar, 1989b, 1989a] ... 

Lu, P. and Lee, K. (2003). An alternative derivation of dynamic admittance matrix of piezoelectric cantilever bimorph. Journal of Sound and Vibration 266, pp. 723-735. 

Position-based impedance controller, x is the robot actual pose in the task space computed from the actual joint configuration q with the FK block, Xj is the desired pose in the task space, x, is the equiUbritim pose of the environment, K, is the net stiffness of the sensor and of the environment, f, is the external environment forces expressed in the task space, fj is the desired force vector, is the desired joint configuration computed with the inverse kinematic (IK) block, and is the commanded motor torque vector. The command trajectory x is defined as s.x,. = Z" (fj - O, where Z is the admittance matrix and s is the argument of the Laplace transform. 

Adjoint network A network having a nodal admittance matrix which is the transpose of that of a given network. This concept is useful in deriving current-mode networks from voltage-mode networks. 

The Laplacian matrix is sometimes also called the Kirchhojf matrix (Mohar, 1989 Kunz, 1992, 1993, 1995) due to its role in the matrix-tree theorem (Cvetkovic et al., 1995), implicit (Moon, 1970) in the electrical network work of Kirchhoff (1847 in his paper Kirchhoff also introduced the concept of the spanning tree, though he did not use this term). It is also known as the admittance matrix (Cvetkovic et al., 1995). However, the name Laplacian matrix appears to be more appropriate since this matrix is just the matrix of a discrete Laplacian operator, which is one of the basic differential operators in quantum chanistry and beyond. Below we give the Laplacian matrix of the vertex-labeled graph Gj (see structured in Figure 2.1) ... 

As is well known, all alternating current (AC) power systems are basically three-phase circuits. This fact makes voltage, current, and impedance a 3-D matrix form. A symmetrical component transformation (i.e., Fortescue and Clarke transformations) is well known to deal with three-phase voltages and currents. However, the transformation cannot diagonalize an n X n impedance/admittance matrix. In general, modal theory is necessary to deal with an untransposed transmission line. In this chapter, modal theory is explained. By adopting modal... 

Equation 1.112 shows that the proportion of current to voltage at any point on a semiinfinite line, that is, the characteristic admittance matrix, is defined as follows ... 

This equation produces the same matrices as in Equation 1.113. For example, for the characteristic admittance matrix ... 

Let us define matrix P as a product of series impedance matrix Z and shunt admittance matrix 7 for a multiconductor system ... 

It is clear from Equation 1.265 that once the node conductance matrix is composed, the solution of the voltages is obtained by taking the inverse of the matrix, as the current vector (J) is known. In the nodal analysis method, the composition of the nodal conductance is rather straightforward, as is well known in circuit theory. In general, nodal analysis gives a complex admittance matrix because of jcoL and jcoC. 

The admittance matrix is expressed in the following form using the potential coefficient matrix ... 

The impedance matrix [Z"] and the admittance matrix [F ] are 4x4 matrices composed of three cores and a reduced single sheath. 

In the same manner, the reduced admittance matrix becomes ... 

---