вихревая аутентификация работает, но я не могу достигнуть других страниц

Это может быть связано с перенаправленным во время авторизации. См. -L и - Доверенные параметра в Человек Curl . Также попробуйте тестирование -W Redirect_url , чтобы увидеть фактическую страницу, которую вы будете перенаправлены, если это так.

   -L, --location
          (HTTP/HTTPS) If the server reports that the requested page has  moved  to  a  different  location
          (indicated  with a Location: header and a 3XX response code), this option will make curl redo the
          request on the new place. If used together with -i, --include or -I,  --head,  headers  from  all
          requested  pages  will  be shown. When authentication is used, curl only sends its credentials to
          the initial host. If a redirect takes curl to a different host, it won't be able to intercept the
          user+password.  See  also  --location-trusted  on how to change this. You can limit the amount of
          redirects to follow by using the --max-redirs option.

          When curl follows a redirect and the request is not a plain GET (for example  POST  or  PUT),  it
          will  do  the  following  request  with  a  GET if the HTTP response was 301, 302, or 303. If the
          response code was any other 3xx code, curl will re-send the  following  request  using  the  same
          unmodified method.

   --location-trusted
          (HTTP/HTTPS)  Like  -L,  --location, but will allow sending the name + password to all hosts that
          the site may redirect to. This may or may not introduce a security breach if the  site  redirects
          you  to  a  site to which you'll send your authentication info (which is plaintext in the case of
          HTTP Basic authentication).

   -w, --write-out <format>
          Defines what to display on stdout after a completed and successful operation.  The  format  is  a
          string  that  may contain plain text mixed with any number of variables. The string can be speci‐
          fied as "string", to get read from a particular file you specify it "@filename" and to tell  curl
          to read the format from stdin you write "@-".

          The  variables  present  in  the output format will be substituted by the value or text that curl
          thinks fit, as described below. All variables are specified as %{variable_name} and to  output  a
          normal  % you just write them as %%. You can output a newline by using \n, a carriage return with
          \r and a tab space with \t.

          NOTE: The %-symbol is a special symbol in the win32-environment, where all occurrences of %  must
          be doubled when using this option.

          The variables available are:


          redirect_url   When  an  HTTP request was made without -L to follow redirects, this variable will
                         show the actual URL a redirect would take you to. (Added in 7.18.2)