Eulerszögek

Eulerszögek, also known as Euler angles, are a set of three successive rotational transformations that are used to define the orientation of a rigid body in three-dimensional space. They are commonly employed in fields such as physics, engineering, and computer graphics. The angles represent rotations around specific axes, typically denoted as x, y, and z, or in a fixed or intrinsic coordinate system.

There are several conventions for defining Euler angles, leading to different sequences of rotations. A common convention is the Z-Y-Z convention, where the first rotation is around the z-axis, the second around the new y-axis, and the third around the final z-axis. Other conventions include Z-X-Z, Y-X-Y, and X-Y-Z, among many others. The choice of convention depends on the specific application and the desired properties of the transformation.

While Euler angles are intuitive for representing orientations, they are prone to a phenomenon called gimbal lock. Gimbal lock occurs when two of the three rotational axes become aligned, effectively reducing the number of degrees of freedom and making it impossible to rotate around one of the axes. This can be a significant issue in applications requiring continuous and unrestricted rotation.

Despite the limitation of gimbal lock, Euler angles remain a valuable tool for representing and manipulating orientations in many scenarios. They are often used for visualizing rotations and for setting initial conditions in simulations. For applications where gimbal lock is a critical concern, alternative representations like quaternions or rotation matrices are often preferred.