The complex configuration of helicopter guarantees that the vehicle modeling, trim and simulation are significantly more difficult than fixed-wing aircrafts. In this paper, general expressions for aerodynamic forces and moments, acting on helicopter due to its main and tail rotors at any flight conditions, are derived by using momentum and blade element theories. These complex expressions are inserted in the rigid body equations of motion, derived from Newton second law, to build a generic nonlinear mathematical model for single main and tail rotors helicopters; in order to obtain their responses to arbitrary control inputs. This model can be used in pilot training, control system design, and studying the helicopter stability characteristics. Trimming problem is solved at general flight conditions; arbitrary turn rate, flight path and side slip angles. The power required to fly helicopter at forward flight with several flight path angles is determined. The flight path angle required for helicopter autorotation condition is calculated at any forward speed. The mathematical model is solved by numerical integration (Runge-Kutta method) in the simulation code. The resulting trim conditions are verified by supplying the trim control inputs to the simulation code and verifying that the helicopter is flying in steady-state.