 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
ssrs 2014 barcode Satellite Mobile and Specialized Services Dennis Roddy in Software
Satellite Mobile and Specialized Services Dennis Roddy QR Code Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Printing QR Code In None Using Barcode encoder for Software Control to generate, create QR Code image in Software applications. Conic Sections
QR Code Decoder In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Drawing QR Code In C#.NET Using Barcode generation for Visual Studio .NET Control to generate, create Quick Response Code image in .NET framework applications. A conic section, as the name suggests, is a section taken through a cone. At the intersection of the sectional plane and the surface of the cone, curves having many different shapes are produced, depending on the inclination of the plane, and it is these curves which are referred to generally as conic sections. Although the origin of conic sections lies in solid geometry, the properties are readily expressed in terms of plane geometrical curves. In Fig. B.1a, a reference line for conic sections, known as the directrix, is shown as ZD. The axis for the conic sections is shown as line ZZ . The axis is perpendicular to the directrix. The point S on the axis is called the focus. For all conic sections, the focus has the particular property that the ratio of the distance SP to distance PQ is a constant. SP is the distance from the focus to any point P on the curve (conic section), and PQ is the distance, parallel to the axis, from point P to the directrix. The constant ratio is called the eccentricity, usually denoted by e. Referring to Fig. B.1a, Generating Quick Response Code In VS .NET Using Barcode creator for ASP.NET Control to generate, create QR Code image in ASP.NET applications. Creating QR Code JIS X 0510 In VS .NET Using Barcode generation for VS .NET Control to generate, create QR Code ISO/IEC18004 image in Visual Studio .NET applications. (B.1) QR Code ISO/IEC18004 Encoder In VB.NET Using Barcode generator for .NET Control to generate, create QR Code image in Visual Studio .NET applications. Create Bar Code In None Using Barcode generation for Software Control to generate, create bar code image in Software applications. The conic sections are given particular names according to the value of e, as shown in the following table: UPC Code Encoder In None Using Barcode encoder for Software Control to generate, create Universal Product Code version A image in Software applications. Generate Code39 In None Using Barcode encoder for Software Control to generate, create USS Code 39 image in Software applications. Curve
GS1128 Maker In None Using Barcode creation for Software Control to generate, create GS1 128 image in Software applications. Making Barcode In None Using Barcode generator for Software Control to generate, create bar code image in Software applications. Ellipse Parabola Hyperbola
ISBN  13 Drawer In None Using Barcode drawer for Software Control to generate, create ISBN  13 image in Software applications. Encode Data Matrix In Java Using Barcode generator for Java Control to generate, create DataMatrix image in Java applications. Eccentricity, e
Making ECC200 In Visual Basic .NET Using Barcode encoder for .NET Control to generate, create ECC200 image in Visual Studio .NET applications. UPCA Maker In None Using Barcode generator for Font Control to generate, create UPC Symbol image in Font applications. e<1 e=1 e>1
Scanning Barcode In Java Using Barcode Control SDK for BIRT Control to generate, create, read, scan barcode image in BIRT applications. Encoding GTIN  13 In C# Using Barcode creator for .NET Control to generate, create GS1  13 image in Visual Studio .NET applications. Satellite Mobile and Specialized Services Dennis Roddy
Encode GS1  13 In .NET Framework Using Barcode generator for .NET framework Control to generate, create GTIN  13 image in VS .NET applications. Encode EAN 13 In Visual Basic .NET Using Barcode creator for .NET Control to generate, create UPC  13 image in .NET applications. Figure B.1
Satellite Mobile and Specialized Services Dennis Roddy
These curves are encountered in a number of situations. In this book they are used to describe: 1. The path of satellites orbiting the earth 2. The ellipsoidal shape of the earth 3. The outline curves for various antenna reflectors A polar equation for conic sections with the pole at the foci can be obtained in terms of the fixed distance p, called the semilatus rectum. The polar equation relates the point P to the radius r and the angle Fig. B.1b). From Fig. B.1b, (B.2) Also, (B.3) Combining Eqs. (B.2) and (B.3) and simplifying gives the polar equation as
(B.4) If the angle is measured from SA, shown as in Fig. B.1c, then, since = 180 + , the polar equation becomes (B.5) The Ellipse
For the ellipse, e < 1. Referring to Eq. (B.4), when = 0 , r = p/(1 e). Since e < 1, r is positive. At = 90 , r = p, and at = 180 , r = p/(1 + e). Thus r decreases from a maximum of p/(1 e) to a minimum of r = p/(1 + e), the locus of r describing the closed curve A BMA (Fig. B.2). Also, since cos( ) = cos , the curve is symmetrical about the axis, and the closed figure results (Fig. B.2a). The length AA is known as the major axis of the ellipse. The semimajor axis a = AA /2 and e are the parameters normally specified for an ellipse. The semilatus rectum p can be obtained in terms of these two quantities. As already shown, the maximum value for r is SA = p/(1 e) and the Satellite Mobile and Specialized Services Dennis Roddy
Figure B.2 minimum value is SA = p/(1 + e). Adding these two values gives
Satellite Mobile and Specialized Services Dennis Roddy
Since a = AA /2, it follows that
(B.6) Substituting this into Eq. (B.5) gives
(B.7) which is Eq. (2.23) of the text. Equation (B.7) can be written as
When = 360 , (B.8) which is Eq. (2.6) of the text. When = 180
(B.9) which is Eq. (2.5) of the text. Referring again to Fig. B.2a, and denoting the length SO = c, it is seen that AS + c = a. But, as shown above, AS = p/(1 + e) and p = a(1 e2). Substituting these for AS and simplifying gives (B.10) Point O bisects the major axis, and length BO is called the semiminor axis, denoted by b (BB is the minor axis) (Fig. B.2b). The semiminor axis can be found in terms of a and e as follows: Referring to Fig. B.2b, 2a = SA + SA = e(AZ + A Z) = e(2OZ), and therefore, (B.11) But OZ = BC = SB/e, and therefore, SB = a. SB is seen to be the radius at B. From the rightangled triangle so formed,

