This paper studies the modeling and control of quadcopter. It models the quadcopter nonlinear dynamics using Lagrange formalism and design controller for attitude (pitch & roll), heading & altitude regulation of quadrotor. Mathematical modeling includes aerodynamic effects and gyroscopic moments. One Non-linear Control strategy, Third-Order SMC based on a super-twisting algorithm has been proposed. Third-Order SMC Controller is designed for regulation control problem with the four control variables. The Controller has been implemented on the quadrotor physical model using Matlab/Simulink software. Finally, the performance of the proposed controller was demonstrated in the simulation study. The simulation results show excellent modeling and control performance. Index Terms-HOSMC, Lagrange, Mathematical Modelling, Quadrotor, MATLAB/Simulink. 1. INTRODUCTION An Unmanned Aerial Vehicle (UAV) refers to a flying machine without an on-board human pilot , . These vehicles are being increasingly used in many civil domains, especially for surveillance, environmental researches, security, rescue, and traffic monitoring. Under the category of rotorcraft UAVs, Quadrotor has acquired much attention among researchers. The quadrotor is a multi-copter that is lifted and propelled by four rotors, each mounted on one end of a cross-like structure. Each rotor consists of a propeller fitted to a separately powered Brushless DC motor. The quadcopter has six degrees of freedom (three translational and three rotational) and only four actuators . Hence, the quadcopter is an underactuated, highly nonlinear, and coupled system. Several linear control approaches, such as PID, Linear Quadratic Regulator (LQR), and Linear Quadratic Gaussian(LQG), have been proposed in the literature and applied for attitude stabilization and/or altitude tracking of Quadrotors, . However, these methods can impose limitations on the application of quadrotors for extended flight Regions, i.e., aggressive maneuvers, where the system is no longer linear. Moreover, the stability of the closed-loop system can only be achieved for small regions around the equilibrium point, which are extremely hard to compute. Besides, the performances of these control laws on attitude stabilization are not satisfactory enough compared with other more advanced methods. To overcome this problem, nonlinear control alternatives, such as feedback linearization, SMC , , , and Backstepping  approaches are recently used in the VTOL aircraft control framework. An integral predictive nonlinear H∞ strategy has been also proposed and applied by G.V. Raffo et al. in . In summary, the literature on quadrotor control ignores the aerodynamic effects, air disturbance, and gyroscopic moments in the dynamic modeling of the quadrotor. Besides, in the case of sliding mode controller implementation, it does not reduce both the control effort and the chattering effect. This paper uses a novel approach to address the above problems. It also designed a novel Third-order SMC controller with minimum tracking error. The paper is organized into five sections. In section 1, it introduces quadrotor UAV. In Section 2, it models the physical system by considering the aerodynamic and gyroscopic effects. In Section 3, it designs second-order SMC based on the supertwisting algorithm. In Section 4, present the simulation results obtained from the control implementation of the physical system in the Simulink environment. Finally, in Section 5, it shows the control inputs and then concludes the work. 2. MATHEMATICAL MODELLING In this section, a complete dynamical model of the Quadrotor UAV is established using the Lagrange formalism. 2.1 Rotational Matrix The orientation of the quadrotor is represented by Euler angles (pitch, roll, and yaw).To transform the body-fixed frame into the inertial frame; the z-y-x rotational matrix is considered .