Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the 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 orientations), in contrast to rotation around a axis.
The special case of a rotation with an internal axis passing through the body's own center of mass is known as a spin (or autorotation). In that case, the surface intersection of the internal spin axis can be called a pole; for example, Earth's rotation defines the geographical poles.
A rotation around a completely external axis is called a revolution (or orbit), e.g. Earth's orbit around the Sun. The ends of the external axis of revolution can be called the orbital poles.
Either type of rotation is involved in a corresponding type of angular velocity (spin angular velocity and orbital angular velocity) and angular momentum (spin angular momentum and orbital angular momentum).
Rotation (mathematics)
Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps at least one point fixed. This definition applies to rotations in two dimensions (in a plane), in which exactly one point is kept fixed; and also in three dimensions (in space), in which additional points may be kept fixed (as in rotation around a fixed axis, as infinite line).
All rigid body movements are rotations, translations, or combinations of the two.
A rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion. The axis is perpendicular to the plane of the motion.
If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results. The reverse (inverse) of a rotation is also a rotation. Thus, the rotations around a point/axis form a group.
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Etudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs variables.
Étudier les concepts fondamentaux d'analyse, et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables.
Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Classic Euler angles usually take the inclination angle in such a way that zero degrees represent the vertical orientation. Alternative forms were later introduced by Peter Guthrie Tait and George H.
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.
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 below, the matrix rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: If x and y are the endpoint coordinates of a vector, where x is cosine and y is sine, then the above equations become the trigonometric summation angle formulae.
Organisé en deux parties, ce cours présente les bases théoriques et pratiques des systèmes d’information géographique, ne nécessitant pas de connaissances préalables en informatique. En suivant cette
Organisé en deux parties, ce cours présente les bases théoriques et pratiques des systèmes d’information géographique, ne nécessitant pas de connaissances préalables en informatique. En suivant cette
The present invention concerns a pivot comprising two assemblies, namely a central assembly (401) and a peripheral assembly (400). These two assemblies are mobile in rotation relative to each other around an axis of rotation (A). The pivot is characterized ...
2024
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