Add/Remove class on scroll depending on scroll length
The code can made very short.

$(window).scroll(function () {
    var scrollTop = $(document.body).hasClass('home') ? 510 : 293;
    $('#navigation-wrapper').toggleClass('navbar-fixed-top', $(this).scrollTop() &gt; scrollTop);
});



There is no need of wrapping the code in $(document).ready() for binding events on window.
Use ternary operator
Use toggleClass() with second parameter to add/remove class based on a condition.