A drilling rig system with a main shaft or shaft-like structure driven directly by an AC motor; the system in one aspect for pumping fluid (e.g., but not limited to, drilling fluid), the system having, in certain aspects, pump apparatus with a pumping section and a motor section, the pumping section having an inlet and an outlet, the motor section having a drive shaft for connection to a pump pinion shaft for reciprocating in and out of the pumping section to alternately suck fluid into the inlet and pump fluid out the outlet, and the motor being directly connected to the pump pinion shaft, and methods for using such a system.