Hacer login programaticamente contra j_security_check

Os adjunto un codigo para hacer login programaticamente contra un servidor con seguridad estandar de Java (un tomcat para ser exacto).

Con este codigo, el ultimo System.out.print muestra una pagina protegida (en el ejemplo index.html esta protegida)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.net.HttpURLConnection;
import java.net.MalformedURLException;
import java.net.URL;




public class Cliente {
    
public static void main(String[] agrs) throws MalformedURLException, 
IOException {
           
    HttpURLConnection connection = (HttpURLConnection) new URL("http://localhost:8080/servletname/index.html").openConnection();
        connection.setInstanceFollowRedirects(false);
        
        BufferedReader reader = new BufferedReader(new InputStreamReader(connection.getInputStream()));
        reader.close();
        
        String cookie = connection.getHeaderField("Set-Cookie");
        cookie = cookie.substring(0, cookie.lastIndexOf(';'));
        String location = "http://localhost:8080/servletname/j_security_check?j_username=a&j_password=a";
        connection = (HttpURLConnection) new URL(location).openConnection();
        connection.setRequestMethod("POST");
        connection.setRequestProperty("Cookie", cookie);
        connection.setInstanceFollowRedirects(false);
        
       
        location = connection.getHeaderField("Location");
        connection = (HttpURLConnection) new URL(location).openConnection();
        connection.setRequestProperty("Cookie", cookie);
        connection.setInstanceFollowRedirects(true);
       
       BufferedReader in = new BufferedReader(new InputStreamReader(
                                    connection.getInputStream()));
        String inputLine;
        while ((inputLine = in.readLine()) != null) 
            System.out.println(inputLine);

       }    
}