Mathematical model of Quadcopter?

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I want to know how to make the mathematical model of Quadcopter? Is there any differential equation for quadcopter? I want to simulate quadcopter as a mathematical model so I want to know how can I make equations to convert the Speed of motors into the desired yaw, pitch and roll to achieve desired real world x,y,z coordinates. Please help if any body know any reference or direct code that simulates the quadcopter.

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Yes, there are. See the fantastic paper by Lee, Leok, and McClamroch:

http://math.ucsd.edu/~mleok/pdf/LeLeMc2010_quadrotor.pdf

See equations (2)-(5).