a:4:{s:8:"template";s:10276:"<!DOCTYPE html>
<html lang="en-US">
<head>
<meta charset="utf-8"/>
<meta content="width=device-width, initial-scale=1" name="viewport"/>
<link href="http://gmpg.org/xfn/11" rel="profile"/>

<title>{{ keyword }}</title>

<style id="cleanwp-maincss-css" media="all" rel="stylesheet" type="text/css">

/* Reset
-------------------------------------------------------------- */
html,body,div,h1,h2,a,ul,li,footer,header,nav {
    border: 0;
    font-family: inherit;
    font-size: 100%;
    font-style: inherit;
    font-weight: inherit;
    margin: 0;
    outline: 0;
    padding: 0;
    vertical-align: baseline;
}

html {
    font-family: sans-serif;
    font-size: 62.5%;
    overflow-y: scroll;
    -webkit-text-size-adjust: 100%;
    -ms-text-size-adjust: 100%;
}

*,*:before,*:after {
    -webkit-box-sizing: border-box;
    -moz-box-sizing: border-box;
    box-sizing: border-box;
}

body {
    background: #fff;
    line-height: 1;
}

footer,header,nav {
    display: block;
}

ul {
    list-style: none;
}

a {
    background-color: transparent;
}

a:focus {
    outline: thin dotted;
}

a:hover,a:active {
    outline: 0;
}

button {
    color: inherit;
    font: inherit;
    margin: 0;
}

button {
    overflow: visible;
}

button {
    text-transform: none;
}

button {
    -webkit-appearance: button;
    cursor: pointer;
}

button::-moz-focus-inner {
    border: 0;
    padding: 0;
}

/* Typography & Elements
-------------------------------------------------------------- */
body,button {
    color: #161514;
    font-family: Lora,Arial,sans-serif;
    font-size: 14px;
    line-height: 1.6;
}

button {
    max-width: 100%;
}

body {
    background: #717171;
}

a {
    color: #C90000;
    text-decoration: none;
    outline: none;
}

a:hover {
    color: #111111;
    text-decoration: none;
}

a:focus {
    outline: none;
}

h1,h2 {
    clear: both;
    font-family: 'Raleway',Arial,sans-serif;
    font-weight: 700;
    line-height: 1;
    margin: .6em 0;
}

h1 {
    font-size: 36px;
}

h2 {
    font-size: 24px;
}

ul {
    margin: 0 0 1.5em 3em;
}

ul {
    list-style: disc;
}

/* Clearings & Accessibility
-------------------------------------------------------------- */
.clear {
    clear: both;
}

.clearfix:before,.clearfix:after {
    content: " ";
    display: table;
}

.clearfix:after {
    clear: both;
}

.screen-reader-text {
    clip: rect(1px,1px,1px,1px);
    position: absolute!important;
    height: 1px;
    width: 1px;
    overflow: hidden;
}

.screen-reader-text:focus {
    background-color: #f1f1f1;
    border-radius: 3px;
    box-shadow: 0 0 2px 2px rgba(0,0,0,0.6);
    clip: auto!important;
    color: #21759b;
    display: block;
    font-size: 14px;
    font-weight: 700;
    height: auto;
    left: 5px;
    line-height: normal;
    padding: 15px 23px 14px;
    text-decoration: none;
    top: 5px;
    width: auto;
    z-index: 100000;
}

/* Forms
-------------------------------------------------------------- */
button {
    font-size: 100%;
    margin: 0;
    vertical-align: baseline;
}

button {
    border: 1px solid;
    border-color: #ccc #ccc #bbb;
    border-radius: 3px;
    background: #e6e6e6;
    -webkit-box-shadow: inset 0 1px 0 rgba(255,255,255,0.5),inset 0 15px 17px rgba(255,255,255,0.5),inset 0 -5px 12px rgba(0,0,0,0.05);
    -moz-box-shadow: inset 0 1px 0 rgba(255,255,255,0.5),inset 0 15px 17px rgba(255,255,255,0.5),inset 0 -5px 12px rgba(0,0,0,0.05);
    box-shadow: inset 0 1px 0 rgba(255,255,255,0.5),inset 0 15px 17px rgba(255,255,255,0.5),inset 0 -5px 12px rgba(0,0,0,0.05);
    color: rgba(0,0,0,.8);
    cursor: pointer;
    -webkit-appearance: button;
    font-size: 12px;
    line-height: 1;
    padding: .6em 1em .4em;
    text-shadow: 0 1px 0 rgba(255,255,255,0.8);
}

button:hover {
    border-color: #ccc #bbb #aaa;
    -webkit-box-shadow: inset 0 1px 0 rgba(255,255,255,0.8),inset 0 15px 17px rgba(255,255,255,0.8),inset 0 -5px 12px rgba(0,0,0,0.02);
    -moz-box-shadow: inset 0 1px 0 rgba(255,255,255,0.8),inset 0 15px 17px rgba(255,255,255,0.8),inset 0 -5px 12px rgba(0,0,0,0.02);
    box-shadow: inset 0 1px 0 rgba(255,255,255,0.8),inset 0 15px 17px rgba(255,255,255,0.8),inset 0 -5px 12px rgba(0,0,0,0.02);
}

button:focus,button:active {
    border-color: #aaa #bbb #bbb;
    -webkit-box-shadow: inset 0 -1px 0 rgba(255,255,255,0.5),inset 0 2px 5px rgba(0,0,0,0.15);
    -moz-box-shadow: inset 0 -1px 0 rgba(255,255,255,0.5),inset 0 2px 5px rgba(0,0,0,0.15);
    box-shadow: inset 0 -1px 0 rgba(255,255,255,0.5),inset 0 2px 5px rgba(0,0,0,0.15);
}

/* Layout
-------------------------------------------------------------- */
#wrapper {
    margin: 0 auto;
    position: relative;
}

#content {
    padding: 15px;
    width: 1030px;
    margin: 0 auto;
    background: #faf9f5;
    border-bottom: 1px solid #ddd;
}

/* Header
-------------------------------------------------------------- */
#masthead {
    background: #faf9f5;
    margin: 10px auto 0;
    padding: 10px 15px 10px 15px;
    width: 1030px;
}

#site-top {
    margin: 0;
    position: relative;
    overflow: hidden;
}

#blogname {
    margin: 0 0 10px 0;
    padding: 0;
    overflow: hidden;
}

.site-title {
    margin: 0 0 10px 0;
    text-align: center;
    font-size: 36px;
    font-weight: bold;
    color: #000000;
}

.site-title a {
    display: block;
    color: #000000;
}

.site-description {
    margin: 0 0 0 0;
    text-align: center;
    font-size: 18px;
    font-weight: bold;
    color: #000000;
}

.header-social-icons {
    font-family: Lora;
    font-size: 20px;
    padding: 10px 0 10px;
    text-align: center;
    line-height: 1;
}

/* Menu
-------------------------------------------------------------- */
.main-navigation {
    background-color: #777;
    display: block;
    padding: 0 10px;
    font-family: 'Raleway';
}

.main-navigation ul {
    list-style: none;
    margin: 0;
}

.main-navigation li {
    float: left;
    padding: 0;
    position: relative;
}

.main-navigation a {
    color: #fff;
    display: block;
    font-size: 13px;
    font-weight: bold;
    text-decoration: none;
    text-transform: uppercase;
    -webkit-transition: all .2s ease;
    transition: all .2s ease;
    padding: 10px;
}

.main-navigation a:hover {
    color: #ccc;
}

.menu-toggle {
    cursor: pointer;
    display: none;
}

@media screen and (max-width: 1049px) {
.menu-toggle {
    font-family: 'Raleway';
    font-weight: bold;
    background: none;
    border: none;
    -webkit-border-radius: 0;
    -moz-border-radius: 0;
    border-radius: 0;
    -webkit-box-shadow: none!important;
    -moz-box-shadow: none!important;
    box-shadow: none!important;
    color: #fff;
    display: block;
    font-size: 16px;
    margin: 0 auto;
    padding: 10px;
    text-align: center;
    text-shadow: none;
    text-transform: uppercase;
    width: 100%;
}

.menu-toggle:before {
    display: inline-block;
    font-family: FontAwesome;
    font-size: 16px;
    font-weight: normal;
    line-height: 1;
    vertical-align: text-bottom;
    -webkit-font-smoothing: antialiased;
    content: "\f0c9";
    margin-right: 12px;
    position: relative;
    top: -2px;
}

.menu-toggle {
    display: block;
}

.main-navigation {
    color: #fff;
    padding-right: 1em;
    padding-left: 1em;
}

.main-navigation ul {
    display: none;
}

.main-navigation ul a {
    font-size: 16px;
    text-transform: uppercase;
}

.main-navigation ul li {
    border-top: 0px dotted #5d5c5c;
    float: none;
    padding: 0;
}

.main-navigation ul li:first-child {
    border-top: 0;
}
}


.site-footer {
    width: 1030px;
    margin: 0 auto;
    padding: 20px 0 20px 0;
    background: #ddd;
    font-size: 90%;
}

.site-footer a:link,.site-footer a:visited {
}

.site-footer a:hover {
}

.site-info {
    text-align: center;
    line-height: 16px;
}


@media only screen and (max-width: 1049px) {
#content {
    width: 100%;
}

#masthead {
    width: 100%;
    padding: 10px 0 10px 0;
}

.site-title {
    padding-left: 10px;
    padding-right: 10px;
}

.site-description {
    padding-left: 10px;
    padding-right: 10px;
}

.site-footer {
    width: 100%;
}

.site-info {
    width: 100%;
}
}</style>
<style id="font-awesome-css" media="all" rel="stylesheet" type="text/css">/*!
 *  Font Awesome 4.5.0 by @davegandy - http://fontawesome.io - @fontawesome
 *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)
 */@font-face{font-family:'FontAwesome';src:url() format('embedded-opentype'),url(),url(),url(),url();font-weight:normal;font-style:normal}
</style>
<link href="//fonts.googleapis.com/css?family=Lora:400,700,400italic,700italic|Raleway:700,900,400,300&amp;subset=latin,latin-ext" id="cleanwp-webfont-css" media="all" rel="stylesheet" type="text/css"/>


<style type="text/css">
                                                                           		.entry-title a:hover {color: #444444}
                                                                                                                                                      															.entry-read-more {display: none;}
			</style>
<style id="custom-background-css" type="text/css">
body.custom-background { background-color: #777777; }
</style>
</head>
<body class="custom-background">
<div id="wrapper">
<a class="skip-link screen-reader-text" href="#">Skip to content</a>
<header class="site-header" id="masthead" role="banner">
<div id="site-top">
<div id="blogname">
<div class="site-branding">
<h1 class="site-title"><a href="#" rel="home">{{ keyword }}</a></h1>
<h2 class="site-description">The Internet It Just Gives and Gives and Gives.</h2>
</div>
</div>
<div class="header-social-icons">
</div>
</div>
<nav class="main-navigation clearfix" id="site-navigation" role="navigation">
<button aria-controls="primary-menu" aria-expanded="false" class="menu-toggle">Menu</button>
<div class="menu" id="primary-menu"><ul><li><a href="#">Home</a></li></ul></div>
</nav>
</header>
<div class="site-content" id="content">

{{ text }}

<div class="clear"></div>
</div>
</div>
<footer class="site-footer" id="colophon" role="contentinfo">
<div class="site-info">
  Copyright  2017 {{ keyword }} | <a href="#">Design by ThemesDNA.com</a>
</div>
<div class="clear"></div>
</footer>

</body>
</html>";s:4:"text";s:3491:"In many cases, it is convenient to represent the location of in an alternate set of coordinates, an example of which are the so-called polar coordinates. Usually denoted x, r, or Let consider a figure of vector position below, You certainly can convert $\bf V$ to Cartesian coordinates, it's just ${\bf V} = \frac{1}{x^2 + y^2 + z^2} \langle x, y, z \rangle,$ but computing the divergence this way is slightly messy. Alternatively, you can use the formula for the divergence itself in Finally, a vector in spherical coordinates is described in terms of the parameters r, the polar I have not done this in a while and I am having a brain fart. The magnitude r of the position vector r is (x1 Any vector may be expressed in Cartesian components, by using unit vectors in the directions of ... and the angle between a position vector and a coordinate axis; I have not done this in a while and I am having a brain fart. ... and spherical coordinates (b). Understand the di erence between coordinates and vector components ... their direction changes with position. Understand the di erence between coordinates and vector components ... their direction changes with position. Preliminaries ... and z are the scalar components of the position vector . Any vector can be expressed in terms of them: A~ = A xx^ +Ayy^+Azz^ = Arr^+A^+A``:^ (2) Note the qualitatively new element here: while both ^x;y;^ z^ and ^r;;^ `^ are three mutually orthogonal unit vectors, ^x;y;^ z^ are xed in space but ^r;;^ `^ point in dierent directions according to the direction of The unit vector of a coordinate parameter u is defined in such a way that when a small positive change in u cause the position vector  to change in ^ direction. Calculus and Coordinate systems  In electromagnetics, we will often need to perform integrals ...  A position vector in spherical coordinates at point Finally, a vector in spherical coordinates is described in terms of the parameters r, the polar It is the rate of change of that unit vector with respect to ... though, rather than position. Given: A wheel of radius R rotates with angular velocity Ct 2 k[tex]\hat{}[/tex] (lies Vectors, Vector Calculus, and Coordinate Systems ... positions in space. The key to deriving expressions for curvilinear coordinates is to consider the arc length ... position vector is given by Eq. 1.7 Cylindrical and Spherical Coordinates ... this coordinate system, the position of a point will be given by the ordered pair (r ... VECTORS AND THE GEOMETRY OF SPACE The position vector in cylindrical coordinates becomes r = rur + zk. Gradient of a vector in curvilinear coordinates ... and it provides a gentle introduction to the fact that base vectors can vary with position. Note however that, unlike in the Cartesian representation, we can't use that to tell us where the point is, because we first need to know where the point is to know what vector ##\mathbf e_r## is. spherical coordinates r;;` are also shown. I'm quite comfortable with vector calculus in all sorts of coordinate systems, but for the love of me, I can't seem to figure out where did I go wrong in this simple derivation of the position Coordinate systems are human inventions, ... unit vectors in the spherical coordinate system. We will be able to find these relationships by studying the properties of the position Vectors, Vector Calculus, and Coordinate Systems ... spherical coordinates, ... matrix used to transform a vector from one coordinate system to another is ";s:7:"keyword";s:40:"position vector in spherical coordinates";s:7:"expired";i:-1;}