Aircraft propulsion system and method for operating such a system

A propulsion system for mounting on an aircraft comprising a main body, said propulsion system comprising:

• a first rotating propulsive member and a second rotating propulsive member, the first and second rotating propulsive members adopted for mounting on either side of said main body;
• a transmission box connected to the first rotating propulsive member via a first mechanical shaft and to the second rotating propulsive member via a second mechanical shaft;
• a single gas generator comprising a compressor, a combustion chamber, and a turbine, the single gas generator is configured to produce a thrust of X-Newtons (N) and operatively connect to said transmission box to rotatably drive the first rotating propulsive member and the second rotating propulsive member;
• a single auxiliary turbomachine connected to an electric generator that powers a motor and the motor is operatively connected to at least one of the first rotating propulsive member and the second rotating propulsive member;
• wherein the single auxiliary turbomachine has two operating modes during flight to rotate the first and second rotating propulsive members, including a first operating mode in which the single auxiliary turbomachine is operating and the single gas generator is running and a second operating mode in which the single auxiliary turbomachine is operating and the single gas generator is cut off;
• wherein the single auxiliary turbomachine, when operating, is sized to generate thrust that is less than the thrust of the X-N generated by the single gas generator, and wherein the X-N is a numerical value;
• and
• wherein the motor is directly connected to the transmission box to directly drive the transmission box and the single auxiliary turbomachine is sized to generate thrust of between about 5%-20% of the X-N.