With the development of hardware and control theory, the application of quadcopters is constantly expanding. Quadcopters have emerged in many fields, including transportation, exploration, and object grabbing and placement. These application scenarios require accurate, stable, and rapid control, and a suitable dynamic model is one of the prerequisites. At present, many works are related to it, most of which are modeled using the Newton-Euler method. Some works have also adopted other methods, including the Lagrangian and Hamiltonian methods. This article proposes a new method that solves the Hamiltonian equation of a quadcopter expressed in quasi-coordinate. The external forces and motion of the body are expressed in the quasi-coordinate system of the body, and solved through the Hamiltonian equation. This method simplifies operations and improves computational efficiency. Additionally, a single pendulum is attached to the quadcopter to simulate application scenarios. For the additional single pendulum, it is treated as a particle and the degrees of freedom are constrained by a constraint equation, resulting in a differential algebraic equation. Different operating conditions were set, including stabilization and path flying with no load, and object swinging and path flying with load, for simulation. To achieve effective control, the PID method was adopted. The comparison of the calculation results with the Newton-Euler method proves that the computational complexity of this method is smaller. More specifically, the max improvement in the stabilization and path following are 7.69% and 6.83%, respectively.