You can do this on the command line using ffmpeg
and the crop filter. Handbrake is a great tool, however it uses the same ffmpeg libraries that you can use directly from the command line.
The basic command is as follows:
% ffmpeg -i input_filename -filter:v "crop=w:h:x:y" output_filename
w
= width of the output video
h
= height of the output video
x:y
= coordinate of the top left corner of the crop box (0,0 is top left)
Your specific example, since you want to remove just the top and bottom, you will crop using the center point and just specify the size of the crop box:
% ffmpeg -i input_filename -filter:v "crop=720:480" output_filename
Using some examples from the ffmpeg
page
Crop area 100x100px starting at coordinate (12,34)
% ffmpeg -i input_filename -filter:v "crop=100:100:12:34" output_filename
Same as above, but using the named options
% ffmpeg -i input_filename -filter:v "crop=w=100:h=100:x=12:y=34" output_filename
Crop an area 100x100px from the center point
% ffmpeg -i input_filename -filter:v "crop=100:100" output_filename