Shrinking navigation bar when scrolling down (bootstrap3)

Sticky navbar:

To make a sticky nav you need to add the class navbar-fixed-top to your nav

Official documentation:
https://getbootstrap.com/docs/5.0/components/navbar/#placement

Official example:
http://getbootstrap.com/examples/navbar-fixed-top/

A simple example code:

<nav class="navbar navbar-default navbar-fixed-top" role="navigation">
  <div class="container">
    ...
  </div>
</nav>

with related jsfiddle: http://jsfiddle.net/ur7t8/

Resize the navbar:

If you want the nav bar to resize while you scroll the page you can give a look to this example: http://www.bootply.com/109943

JS

$(window).scroll(function() {
  if ($(document).scrollTop() > 50) {
    $('nav').addClass('shrink');
  } else {
    $('nav').removeClass('shrink');
  }
});

CSS

nav.navbar.shrink {
  min-height: 35px;
}

Animation:

To add an animation while you scroll, all you need to do is set a transition on the nav

CSS

nav.navbar{
  background-color:#ccc;
   // Animation
   -webkit-transition: all 0.4s ease;
   transition: all 0.4s ease;
}

---

I made a jsfiddle with the full example code: http://jsfiddle.net/Filo/m7yww8oa/