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For a quadcopter, diagonally opposite rotors have the same speed and direction which causes it to hover, and adjusting the speed of the rotors give the three basic movements of a flying object, i.e. pitch, roll, yaw.

Similarly, what is the physics behind the tricopter flight control?

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There are few examples of three-rotor helicopters. On of them is the Cierva W.1 Air Horse. According to Wikipedia, torque balance, and hence, yaw control 'was provided by slightly inclining each rotor axis to generate horizontal thrust components to provide anti-torque moments. The three rotor configuration was foreseen by Belgian helicopter experimenter Nicolas Florine in his patent of 1926 which presented the aforementioned means for balancing the reaction on the fuselage of two or more torque driven lifting rotors turning in the same direction.'

https://en.wikipedia.org/wiki/Cierva_Air_Horse

Pitch and roll control was obtained by regulating the lift of the rotors.

https://www.flightglobal.com/pdfarchive/view/1948/1948%20-%202048.html

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