Small Engines (Lawn Mowers, etc.): murray riding lawn mower battery problems, charging systems, battery problems

Question
Sir;
  Is the battery in my riding lawn mower supposed to recharge itself when running? If so how do I fix the problem if the battery is not recharging?

Answer
 Hello Dave:

 With the Engine Running at Full Throttle, Check the Battery and See if it shows Between 12.5VDC and 13.0VDC. If Not, then Send me the Model numbers Off of the Mower and Off of the Engine.  I can then Pull up the Diagrams and See what We are Working on. If Yes, then The Battery has a Dead/Weak Cell. The Engines on Most Mowers with Batteries have Charging Systems that Charge the Battery while the Engine is Running. Thanks.

 Respectfully

 John