## Bodies

FreeDyn handles rigid as well as flexible bodies. The orientation of the bodies are parameterized by the four Euler parameters, which have the advantage that they representation of the orientation is singularity-free, with the disadvantage that an inner constraint has to be realized, since only three orientation parameters are necessary to define the correct orientation.

## Rigid Bodies

Each rigid body has three translational degrees of freedom (DOF) and rotational DOF (Euler parameter), which describe the orientation of the body. The origin of the body coordinate system is located at the center of mass. This decouples the translational movement of the body from the rotational. Moreover, the orientation of the body coordinate system is such that the axes of the body coordinate system are along the principle axes of inertia of the body.

The location of the center of mass represents the initial translational degrees of freedom, while the rotation matrix defines the initial values of the four Euler parameters.

## Flexible Bodies

Each flexible body has three translational, four rotational, and s elastic coordinates. The number s represents the number of shape functions (modes) which are used for the description of the flexibility of the body.

The body coordinate system is attached to the body by a dynamical concept, the so-called Buckens frame, i.e., the frame follows the body such that the origin of the body coordinate system is always located at the center of mass of the body. At the beginning of the simulation the body has to be in its undeformed state. Thus, the initial values of the elastic coordinates are zero. As it is the case for a rigid body, the location of the center of mass of the undeformed body represents the initial translational degrees of freedom, while the rotation matrix defines the initial values of the rotational parameter.