| 单词 | closed curve |
| 例句 | Recall that if vector field F is conservative, then F does no work around closed curves—that is, the circulation of F around a closed curve is zero. Calculus, Volume 3 2016-03-30T00:00:00Z A closed curve doubles whatever is inside it. The Same, Only Different 2018-04-04T04:00:00Z In a perfect fluid if this condition is once fulfilled for a closed curve moving with the fluid, it is fulfilled for this curve ever after. Lord Kelvin An account of his scientific life and work 2012-04-06T02:00:32.097Z He suggested first that the planets move around the sun in closed curves, resembling flattened circles, and known as ellipses. Joseph Smith as Scientist A Contribution to Mormon Philosophy 2012-03-12T03:00:27.817Z The principal circumstance which renders the system of Copernicus impossible, is that the orbits of the planets are considered as closed curves around the sun. The Sun changes its position in space therefore it cannot be regarded as being "in a condition of rest" 2012-03-08T03:00:10.827Z These two notions, along with the notion of a simple closed curve, allow us to state several generalizations of the Fundamental Theorem of Calculus later in the chapter. Calculus, Volume 3 2016-03-30T00:00:00Z The lines of force form continuous closed curves running through the interior of the coil; they issue from one end and enter into the other end of the coil, as shown in fig. Hawkins Electrical Guide, Number One Questions, Answers, & Illustrations, A Progressive Course of Study for Engineers, Electricians, Students and Those Desiring to acquire a Working Knowledge of Electricity and its Applications 2011-12-24T03:07:54.823Z He turned it upside down and sideways; it was just a funny closed curve, having neither mathematical nor structural significance. The Romantic Analogue The stars, being displaced always in the line of advance, must similarly appear to describe little closed curves, always a quadrant in advance of the earth, completing their orbits once a year. Pioneers of Science So that, although it may be considered probable, we do not know that it is moving in a closed curve, or will ever again penetrate the precincts of the solar system. A Popular History of Astronomy During the Nineteenth Century Fourth Edition The first consequence is that if F is conservative and C is a closed curve, then the circulation of F along C is zero—that is, ∫CF · dr = 0. Calculus, Volume 3 2016-03-30T00:00:00Z It follows, of course, that the real paths of the planets in space are not closed curves, but spirals of different orders. Myths and Marvels of Astronomy The first wave which reaches a point P consists of longitudinal vibrations, that is, the particle of rock at P moves in a closed curve with its longer axis in the direction FP. A Study of Recent Earthquakes It is clear that if the pulleys are of commensurable diameters, and are rigidly connected — say by belting which neither stretches nor slips — the polishing tool will describe a closed curve. On Laboratory Arts Perhaps the nearest analogy to infinity that we can understand lies in our conception of a closed curve. Four-Dimensional Vistas So we assume the boundary to be a piecewise smooth and continuous simple closed curve. Calculus, Volume 3 2016-03-30T00:00:00Z It has the same value for all closed curves passing just once through the aperture, and it remains constant through all time, whether the solid body be in motion or at rest. Scientific American Supplement, No. 460, October 25, 1884 Thereafter time runs forward, not as schoolmen fable in a straight line, but in a vast closed curve, returning to the place of its starting. Jurgen A Comedy of Justice Given any closed curve, the machine will find its area. Scientific American Supplement, No. 288, July 9, 1881 Other comets, including most of the ``great'' ones, appear to travel in parabolic or, in a few cases, hyperbolic orbits, which, not being closed curves, never bring them back again. Curiosities of the Sky Since the boundary of S is a closed curve, ∫ F · dr is also zero. Calculus, Volume 3 2016-03-30T00:00:00Z That the instantaneous axis travels in a closed curve, and returns to its original position in the body. 2ndly. Five of Maxwell's Papers Kepler had himself assigned no reason why the orbit of a planet should be an ellipse rather than any other of the infinite number of closed curves which might be traced around the sun. Great Astronomers As we have learned, a closed curve is one that begins and ends at the same point. Calculus, Volume 3 2016-03-30T00:00:00Z In fact, if the domain of F is simply connected, then F is conservative if and only if the circulation of F around any closed curve is zero. Calculus, Volume 3 2016-03-30T00:00:00Z The line integral of vector field F along an oriented closed curve is called the circulation of F along C. Circulation line integrals have their own notation: ∮CF · Tds. Calculus, Volume 3 2016-03-30T00:00:00Z That by working the vertical bolts, we can make the axis of the instrument the centre of this closed curve. Five of Maxwell's Papers Recall that a source-free field is a vector field that has a stream function; equivalently, a source-free field is a field with a flux that is zero along any closed curve. Calculus, Volume 3 2016-03-30T00:00:00Z Let C be a closed curve that models a thin wire. Calculus, Volume 3 2016-03-30T00:00:00Z Flux measures the rate that a field crosses a given line; circulation measures the tendency of a field to move in the same direction as a given closed curve. Calculus, Volume 3 2016-03-30T00:00:00Z We first define two special kinds of curves: closed curves and simple curves. Calculus, Volume 3 2016-03-30T00:00:00Z The circulation of a conservative vector field on a simply connected domain over a closed curve is zero. Calculus, Volume 3 2016-03-30T00:00:00Z The flux of a source-free vector field across a closed curve is zero, just as the circulation of a conservative vector field across a closed curve is zero. Calculus, Volume 3 2016-03-30T00:00:00Z To see where the term circulation comes from and what it measures, let v represent the velocity field of a fluid and let C be an oriented closed curve. Calculus, Volume 3 2016-03-30T00:00:00Z |
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