The Analysts will need to either have local accounts on all workstations with Admin rights (not a good thing) or be in some group from the Domain that is also a member of the local admins group.

There may be some other hack or policy to allow Non Admins remote access but not sure and don't feel like searching Google for it right now, but you can if you really need a solution beyond this.

Also, once your Analyst logs in it will log out the current user.