In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains...

squares. Euler's identity may also refer to the pentagonal number theorem. Euler's number, e = 2.71828 . . . , the base of the natural logarithm Euler's idoneal...

right-hand rule. The rotation axis is sometimes called the Euler axis. The axis–angle representation is predicated on Euler's rotation theorem, which dictates...

change when it rotates. Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis...

axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous...

than an actually observed rotation from a previous placement in space. According to Euler's rotation theorem, the rotation of a rigid body (or three-dimensional...

quaternions and Euler angles Davenport chained rotations Euler's rotation theorem Gimbal lock Quaternion Quaternions and spatial rotation Rotation formalisms...

(Miles 1965). Euler–Rodrigues formula Euler's rotation theorem Rodrigues' rotation formula Plane of rotation Axis–angle representation Rotation group SO(3)...

specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem; the magnitude specifies the rotation in radians about that...

the axis of rotation. (Euler's Rotation Theorem). To better understand how "direction cosines" work with quaternions: q w = cos ⁡ ( rotation angle / 2 )...

the axis of rotation (this is Euler's rotation theorem). Each such rotation acts as an ordinary 2-dimensional rotation in the plane orthogonal to this...

_{2}=\omega _{2}+\omega _{1}} . By Euler's rotation theorem, any rotating frame possesses an instantaneous axis of rotation, which is the direction of the...

valid if x is a complex number, and is also called Euler's formula in this more general case. Euler's formula is ubiquitous in mathematics, physics, chemistry...

]} . In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about...

articles Euler's equation of motion and Poinsot's ellipsoid. It follows from Euler's equation that a torque τ applied perpendicular to the axis of rotation, and...

motion can be accomplished in this way due to a theorem by Euler on the existence of an axis of rotation. The displacement D of the center of mass can be...

theorem (geometry) Euler's rotation theorem (geometry) Euler's theorem (differential geometry) Euler's theorem (number theory) Euler's theorem in geometry (triangle...

after Euler's death have recognised his importance in the field as shown by quotes attributed to many of them: Pierre-Simon Laplace expressed Euler's influence...

a rotation by π and a pair of eigenvalues +1 can be identified with a rotation by 0. The special case of n = 3 is known as Euler's rotation theorem, which...

rotation can be interpreted as a rotation by a given angle about a single fixed axis of rotation (see Euler's rotation theorem), and hence it can be simply...

the Euler characteristic of the 2-sphere is two. Therefore, there must be at least one zero. This is a consequence of the Poincaré–Hopf theorem. In the...

useful from a numerical point of view). The Euler equations first appeared in published form in Euler's article "Principes généraux du mouvement des...

guaranteed by the Euler's rotation theorem). All points on a rigid body experience the same angular velocity at all times. During purely rotational motion, all...

Century. The theorem describes the following effect: rotation of an object around its first and third principal axes is stable, whereas rotation around its...

invariant), its Lagrangian is symmetric under continuous rotation: from this symmetry, Noether's theorem dictates that the angular momentum of the system be...

Rotation vectors notation arise from the Euler's rotation theorem which states that any rotation in three dimensions can be described by a rotation by...

constant relative orientation over time. By Euler's theorem, any change in orientation can be described by rotation about an axis through a chosen reference...

prime numbers are distributed. Euler's work in this area led to the development of the prime number theorem. Euler's great interest in number theory...

used. Attitude dynamics and control (spacecraft) Euler's rotation theorem Gyroscope Triad Method Rotation formalisms in three dimensions Geographic coordinate...

vector r i {\displaystyle \mathbf {r} _{i}} is unchanging. By Euler's rotation theorem, we may replace the vector r i {\displaystyle \mathbf {r} _{i}}...