When you create a Dynamic Web Application in Eclipse and run it on Tomcat, the Website will be available trought http://localhost:8080/[PROJECT_NAME]. To “move” the application in the root (making it accessible on http://localhost:8080), go into the project’s properties, go to “Web Project Settings” and just enter “/” in the Context Root textbox. Done.
To restart tomcat, fill the following two lines in a .sh file and make it executable (chmod +x [filename]):
killall -s 9 java
/[tomcat installation folder]/bin/startup.sh
Warning: It kills all other java processes as well!