To do this solely in Apache Tomcat, modify ROOT.war in /webapps/ so that welcome-file (as defined in /WEB-INF/web.xml) points to a JSP that redirects to your desired URL. This JSP can be something like this:
<% response.sendRedirect("/application.do?login_name=username"); %>
You may want to use a forward instead, which would be more efficient but it would not change how the URL looks in the browser location bar. Alternatively, you can use your web server front-end, either a load-balancer like an F5, or Apache HTTP Server with mod_rewrite, to do the redirection without putting load on your Java application server.