I was recently asked how to use the REST API to add nodes to an existing LTM pool. The use case is one where the customer would spin up a new server in Amazon and wanted - by means of an API call - to add it to a pool.
Easy enough. All of the sample calls I have seen to date reference creating the pool simultaneous to creating its members using a POST request.
Note that when you modify the pool, you must specify EVERY member EVERY time. If you only put in one item on the update, all other members will be erased. The same holds true for datagroup updates and any other collection update.
Updated: If you would like to add a member to an existing pool you can do so by specifying the name of the pool in the post to which a new member will be added. This will prepend to the new member to the existing pool. Examples below:
If you POST to tm/ltm/pool//members, it is an addition to the pool members. If you PUT/PATCH to tm/ltm/pool, the whole array you supply in the json input will replace existing members. If you DELETE to tm/ltm/pool//members/, the individual pool_member will be removed.