Eulerkääntöjen

Eulerkääntöjen, also known as Euler rotations, are a set of three consecutive rotations that describe the orientation of a rigid body in three-dimensional space. They are named after the Swiss mathematician Leonhard Euler. These rotations are typically defined by three angles, often denoted as alpha, beta, and gamma, or phi, theta, and psi. The specific order of these rotations matters and defines different Euler angle conventions. Common conventions include ZYZ, XYZ, ZXZ, and others.

The purpose of Euler rotations is to provide a way to represent any arbitrary orientation as a sequence of rotations around specific axes. For instance, in the ZYZ convention, the first rotation is around the Z-axis, followed by a rotation around the new Y-axis, and finally a rotation around the newest Z-axis. This method is widely used in various fields, including computer graphics, robotics, aerospace engineering, and physics, for representing and manipulating the orientation of objects.

While Euler angles are intuitive and easy to visualize for small rotations, they can suffer from a phenomenon called gimbal lock. Gimbal lock occurs when the middle rotation becomes aligned with one of the other rotation axes, effectively reducing the degrees of freedom and making it impossible to rotate around certain axes. This limitation has led to the development of alternative representations for orientation, such as quaternions and rotation matrices, which do not suffer from gimbal lock. Despite this, Euler angles remain a popular choice for certain applications due to their simplicity and ease of understanding.