# Simulate Motion in Six Degrees of Freedom (6DOF)

This example shows how to model six degrees of freedom (6DOF) in Simulink®. The model in this example replicates the motions experienced by an object or vehicle in model in this example replicates axes of rotation (pitch, roll, and yaw) and three axes of translation (heave, surge, and sway). You can switch between using Euler angles and quaternions to model the equations of motion using the representation parameter of the Variant Subsystem block.

This model allows you to analyze the dynamics of aircraft and spacecraft under various conditions without the need for physical prototypes.

### Effect of Body Rotational Rate

The body rotational rates of the Equations of Motion block directly mimic the moment inputs that are fed into the system. These moments are torques applied about the center of mass of the aircraft, influencing its rotational motion around the three axes. You can use these inputs to represent various forces acting on the aircraft, such as aerodynamic forces, engine thrust, or control surface deflections. By accurately modeling these moments, the Equations of motion block can simulate the response of the aircraft in terms of pitch, roll, and yaw rates, providing a realistic representation of its rotational dynamics.

### Type of Aircraft

The 6DoF model is particularly well-suited for modeling combat aircraft, which are designed to operate across a broad range of maneuvers and orientations. Unlike commercial aircraft, combat aircraft must perform extreme maneuvers, including rapid changes in direction and orientation and flying inverted. Being able to simulate motion without constraints on the angles of orientation allows engineers and designers to explore and test the aircraft capabilities in a wide range of scenarios. This unrestricted simulation environment is useful for developing aircraft that can maintain high performance and agility under the most demanding conditions.

### `Equations of Motion` Block and Open-Loop Simulation

The `Equations of Motion` block calculates linear and angular accelerations from the total forces and moments acting on the object , such as an aircraft, then integrates these accelerations to determine velocities and positions over time. In an open-loop setup, you can specify simulation inputs, such as control surface positions or engine output, without any feedback from the current state of the system. This method allows you to analyze the behavior of the object under set conditions, and see the effects of specific inputs on the motion of the object. Open-loop simulations allow you to understand system behavior before moving on to more complex closed-loop control systems, where feedback mechanisms adjust inputs based on the state of the system.

To trim the aircraft around an operating point, see Airframe Trim and Linearize.