Übersetzungen für curl im Englisch» Deutsch-Wörterbuch von PONS Online:curl, to fall in curls, to have a natural curl, curls of smoke. Viele übersetzte Beispielsätze mit "biceps curl" – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen. Übersetzung im Kontext von „curls“ in Englisch-Deutsch von Reverso Context: Her hair is light, and full of curls. Web News Encyclopedia Images Context. To this definition fit naturally. That all comes of my being such a fool as to not remember that wherever you leave a dead snake its mate always comes there and curls live fussball online it. In general curvilinear coordinates not only in Cartesian coordinatesthe curl of curls deutsch cross product of vector fields v and Casino royale novel can be shown casino pypal be. To have or cause to have a curved or sinuous form or surface: My hair has very roulette gewinnen curl in it. At every point in the field, the curl of that point is represented by a vector. You can complete the translation of tight curls given by the English-German Collins dictionary with other dictionaries such as: The curl operator maps continuously differentiable functions f: The hedgehog curled itself up saudi arabien männer a ball. The resulting vector field describing the curl would be uniformly going in the negative z direction. For other uses, see Rotation operator disambiguation. On the other hand, because of the interchangeability of mixed derivatives, e.
Plant Pathology any of various plant diseases characterized by curling of the leaves. Mathematics maths Also called: Usually written curl A , rot A.
Compare divergence 4 , gradient 4. Switch to new thesaurus. Robert Curl , Robert F. Curl , Robert Floyd Curl Jr. To have or cause to have a curved or sinuous form or surface: To move or proceed on a repeatedly curving course: My hair curls easily.
The paper curled up at the edges. My hair has very little curl in it. The hedgehog curled itself up into a ball. References in classic literature?
The equation for each component curl F k can be obtained by exchanging each occurrence of a subscript 1, 2, 3 in cyclic permutation: If x 1 , x 2 , x 3 are the Cartesian coordinates and u 1 , u 2 , u 3 are the orthogonal coordinates, then.
The remaining two components of curl result from cyclic permutation of indices: Suppose the vector field describes the velocity field of a fluid flow such as a large tank of liquid or gas and a small ball is located within the fluid or gas the centre of the ball being fixed at a certain point.
If the ball has a rough surface, the fluid flowing past it will make it rotate. The rotation axis oriented according to the right hand rule points in the direction of the curl of the field at the centre of the ball, and the angular speed of the rotation is half the magnitude of the curl at this point.
The curl of the vector at any point is given by the rotation of a infinitesimal area in the xy -plane for z -axis component of the curl , zx -plane for y -axis component of the curl and yz -plane for x -axis component of the curl vector.
This can be clearly seen in the examples below. In practice, the above definition is rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates , for which simpler representations have been derived.
Such notation involving operators is common in physics and algebra. This expands as follows: Although expressed in terms of coordinates, the result is invariant under proper rotations of the coordinate axes but the result inverts under reflection.
In a general coordinate system, the curl is given by . Equivalently, using the exterior derivative , the curl can be expressed as:.
This formula shows how to calculate the curl of F in any coordinate system, and how to extend the curl to any oriented three-dimensional Riemannian manifold.
Since this depends on a choice of orientation, curl is a chiral operation. In other words, if the orientation is reversed, then the direction of the curl is also reversed.
Upon visual inspection, the field can be described as "rotating". If a stationary object were to be placed in the field with the vectors representing a linear force , the object would rotate clockwise.
The resulting vector field describing the curl would be uniformly going in the negative z direction. It should be noted that the results of this equation align with what could have been predicted using the right-hand rule using a right-handed coordinate system.
Being a uniform vector field, the object described before would have the same rotational intensity regardless of where it was placed.
Upon initial inspection, curl existing in this graph would not be obvious. Using the right-hand rule, it can be predicted that the resulting curl would be straight in the negative z direction.
As predicted, the curl points in the negative z direction when x is positive and vice versa. In general curvilinear coordinates not only in Cartesian coordinates , the curl of a cross product of vector fields v and F can be shown to be.
Another example is the curl of a curl of a vector field. It can be shown that in general coordinates. The vector calculus operations of grad , curl, and div are most easily generalized and understood in the context of differential forms, which involves a number of steps.
In a nutshell, they correspond to the derivatives of 0-forms, 1-forms, and 2-forms, respectively. In 3 dimensions, a differential 0-form is simply a function f x , y , z ; a differential 1-form is the following expression:.
Here the a -coefficients are real functions; the "wedge products", e. The exterior derivative of a 1-form is therefore a 2-form, and that of a 2-form is a 3-form.
On the other hand, because of the interchangeability of mixed derivatives, e.
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