In mathematics, the rotation number is an invariant of homeomorphisms of the circle. It was first defined by Henri Poincaré in 1885, in relation to the...

a unique number called the Carrington Rotation Number, starting from November 9, 1853. (The Bartels Rotation Number is a similar numbering scheme that...

figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary...

degree of the tangential Gauss map. This is called the turning number, rotation number, rotation index or index of the curve, and can be computed as the total...

arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a dimensionless quantity called rotation, defined...

rotation number that is not conjugate to a rotation. Let ƒ: S1 → S1 be an orientation-preserving diffeomorphism of the circle whose rotation number θ...

Arnold) are a pictorial phenomenon that occur when visualizing how the rotation number of a dynamical system, or other related invariant property thereof...

Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an...

In the mathematical theory of dynamical systems, an irrational rotation is a map T θ : [ 0 , 1 ] → [ 0 , 1 ] , T θ ( x ) ≜ x + θ mod 1 , {\displaystyle...

object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric...

{\displaystyle q}  and a rotation number p / q {\displaystyle p/q} . In this context, the attracting cycle of  exhibits rotational motion around a central...

The coin rotation paradox is the counter-intuitive mathematical fact that, when one coin is rolled without slipping around the rim of another coin of equal...

Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe...

geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space. The main use for planes of rotation is in describing...

{\displaystyle \mathbb {T} } is as well. A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized...

Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase...

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention...

Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space...

transformation that substitutes an imaginary-number variable for a real-number variable. Wick rotations are useful because of an analogy between two important...

career development. Job rotation is used systematically by a large number of companies. This can be through structured job rotation programmes, or informally...

Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional...

distinguished by considering their Thurston-Bennequin invariants and rotation number, which are together known as the "classical invariants" of Legendrian...

tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements. A tree rotation moves one...

Rotation, sometimes called rotation pool, 15-ball rotation, or 61, is a pool game, played with a pocketed billiards table, cue ball, and triangular rack...

composition of rotations (i.e. chained rotations). The geometrical definition demonstrates that three consecutive elemental rotations (rotations about the...

orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary...

is slightly different (a common application is the calculation of rotation number). Given a map on a circle, T : S → S {\displaystyle T:{\text{S}}\rightarrow...

change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes...

The rotation curve of a disc galaxy (also called a velocity curve) is a plot of the orbital speeds of visible stars or gas in that galaxy versus their...

Differential rotation is seen when different parts of a rotating object move with different angular velocities (or rates of rotation) at different latitudes...