Gas turbine engine with transmission

A gas turbine engine comprising:

• a low pressure turbine located downstream of and in fluid communication with an exhaust of a high pressure section of the engine, the low pressure turbine having at least one turbine rotor;
• a transmission having a differential having coupled members including a driven member, a driving member, and a selectively rotatable member;
• a low pressure shaft drivingly interconnecting each turbine rotor to the driven member;
• an output shaft drivingly engaged to the low pressure shaft independently of the transmission;
• a low pressure compressor located upstream of and having an exhaust in fluid communication with the high pressure section of the engine, the low pressure compressor having at least one compressor rotor drivingly interconnected to the driving member;
• a first power transfer device engaged to the low pressure shaft for at least one of transferring power thereto and generating power therefrom;
• a second power transfer device engaged to the selectively rotatable member for at least the other of transferring power thereto and generating power therefrom;
• and
• a control unit connecting the first and second power transfer devices and controlling power being transferred therebetween;
• wherein a rotational speed of the selectively rotatable member of the transmission coupled to the driven and driving members determines a variable ratio between rotational speeds of each turbine rotor and of the at least one compressor rotor;
• and
• wherein the second power transfer device is configured to vary the rotational speed of the selectively rotatable member to vary the ratio between the rotational speeds of each turbine rotor and of the at least one compressor rotor, the output shaft being unaffected by the transmission.