Artio works flawlessly on my SSL e-commerce site with virutuemart.
Except:

if I type in www.my_site_name.com or my_site_name.com or my_site_name in the URL address bar, I get:

Found
The document has moved here.
Additionally, a 400 Bad Request error was encountered while trying to use an ErrorDocument to handle the request.

If I type in my_site_name.com there is no problem.

I am not good with htaccess scripting so I need help for a proper redirect of the non SSL info.

My .htaccess reads:

RewriteEngine On
RewriteCond %{SERVER_PORT} !^443$
RewriteRule ^(.*)$ www.my_site_name.com/$1 [R]

RewriteCond %{REQUEST_URI} (/|\.htm|\.php|\.html|/[^.]*)$ [NC]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule (.*) index.php

The first three lines were recommended by the server, the following are recommended by Artio/Joomla...

Please let me know if there is a way to correct this issue so that users can have a seamless redirect from non-SSL addresses in the address bar.