Determination of Coefficients of Capacitance of Regions Bounded By Collinear Sli
Determination of Coefficients of Capacitance of Regions Bounded By Collinear Sli
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In this case it might prove preferable to employ (2, 9), obtaining the fvmction £^{x) to the desired degree of approximation by the method given in [2^, § 6. 3, Extension to More General Regions Since the coefficients of capacitance are conformal invariants, they may be determined by the method described above for any domain which can be mapped confomially onto a slit-domain, A simple example of such a domain is the entire (x, y)-plane slit along a finite number of arcs of a circle (cf, [l], § ...92), By a suitable linear transformation we can map the circumference of this circle onto the x-axis, thus obtaining a slit-domain.
Another domain to which this method applies is a domain bounded externally by one circle and internally by two others. By a suitable linear transformation such a region may always be mapped into a domain with the center of all three circles collinear (cf. Fig. 2), y Figure 2 - 7 - Now suppose that the upper half of this domain, which is simply-connected, is mapped conforraally by an analytic function Y, ' f(z) upon the upper half of the ^-plane.
What to read after Determination of Coefficients of Capacitance of Regions Bounded By Collinear Sli?
You can find similar books in the "Read Also" column, or choose other free books by Bernard Epstein to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In this case it might prove preferable to employ (2, 9), obtaining the fvmction £^{x) to the desired degree of approximation by the method given in [2^, § 6. 3, Extension to More General Regions Since the coefficients of capacitance are conformal invariants, they may be determined by the method described above for any domain which can be mapped confomially onto a slit-domain, A simple example of such a domain is the entire (x, y)-plane slit along a finite number of arcs of a circle (cf, [l], § ...92), By a suitable linear transformation we can map the circumference of this circle onto the x-axis, thus obtaining a slit-domain.
Another domain to which this method applies is a domain bounded externally by one circle and internally by two others. By a suitable linear transformation such a region may always be mapped into a domain with the center of all three circles collinear (cf. Fig. 2), y Figure 2 - 7 - Now suppose that the upper half of this domain, which is simply-connected, is mapped conforraally by an analytic function Y, ' f(z) upon the upper half of the ^-plane.
What to read after Determination of Coefficients of Capacitance of Regions Bounded By Collinear Sli?
You can find similar books in the "Read Also" column, or choose other free books by Bernard Epstein to read onlineMoreLess
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