Vector Analysis: An Introduction to Vector-methods and Their Various Applications to Physics and MathematicsJ. Wiley & Sons, 1911 - 262 من الصفحات Elementary operations of vector analysis -- Scalar and vector products of two vectors -- Vector and scalar products of three vectors -- Differentiation of vectors -- The differential operators -- Applications to electrical theory -- Applications to dynamics, mechanics and hydrodynamics -- Appendix. Notation and formulae. |
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طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
a₁ acceleration angular velocity axis b₁ called Cartesian circuit closed surface components considered const constant vector coördinates curl F curve defined definition denote density differential direction div F Divergence Theorem dt dt electrical ellipsoid equal equation of motion expression F₁ F₂ fluid flux force formula Gauss's Theorem grad Green's Theorem hence hodograph inertia Laplace's Equation line integral magnetic magnitude mass moving space multiplied normal notation obtain operator origin osculating plane parallel particle path perpendicular plane Poisson's Equation potential principal axes quantity r₁ radius vector represented result rigid body rotation scalar function scalar point-function scalar product solid angle sphere surface integral tangent Taylor's Theorem tion unit vector vanishes variable vector function vector product volume w₁ w₂ zero Απ φω дх მა მი მყ
مقاطع مشهورة
الصفحة 22 - A person travelling eastward at the rate of 4 miles per hour, finds that the wind seems to blow directly from the north; on doubling his speed it appears to come from the north-east; find the direction of the wind and its velocity.
الصفحة 26 - CB and CD. Prove that the resultant force is represented in magnitude and direction by four times the line joining the middle points of the diagonals of the quadrilateral.
الصفحة viii - Poinsot has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligible propositions supersede equations".
الصفحة 44 - The squares of the sides of any quadrilateral exceed the squares of the diagonals by four times the square of the line which joins the middle points of the diagonals. Retaining the figure and notation of Ex. 8, Art. 7, we have squares of sides as vectors and squares of diagonals therefore the former sum exceeds the latter by a2 + p° -t- y" - 2Sap - 2 A 2 2J Therefore as lines the same is true.
الصفحة 26 - O is any point in the plane of a triangle ABC, and D, E, F are the middle points of the sides. Show that the system of forces represented by OA, OB, OC is equivalent to the system represented by OD, OE, OF.
الصفحة 24 - ... intersection of corresponding sides lie on a line, then the lines joining the corresponding vertices pass through a common point and conversely. 5. Given a quadrilateral in space. Find the middle point of the line which joins the middle points of the diagonals. Find the middle point of the line which joins the middle points of two opposite sides. Show that these two points are the same and coincide with the center of gravity of a system of equal masses placed at the vertices of the quadrilateral....
الصفحة 23 - P-ft relative to the frame. Obviously this latter is the increase of velocity. EXAMPLES 1. A car is running at 14 miles an hour, and a man jumps from it with a velocity of 8 feet per second in a direction making an angle of 30° with the direction of the car's motion.
الصفحة 23 - ... neglected. Hooke's law only holds within certain limits. If we go on increasing the tension in a string indefinitely, we find that, after a certain limit is passed, Hooke's law ceases to be true, and when a certain still greater tension is reached the string breaks in two parts. EXAMPLES 1. A weight W hangs by a string and is pushed aside by a horizontal force until the string makes an angle of 45° with the vertical. Find the horizontal force and the tension of the string. 2. A weight suspended...
الصفحة i - Vector analysis; an introduction to vector-methods and their various applications to physics and mathematics. Ed.2. 1911. Wiley. "Bibliography,
الصفحة 39 - Af of a force F about a point 0 is defined as the magnitude of F times the perpendicular distance from the point 0 to the line of action of F. If the vector moment M is defined as the vector whose magnitude is M and whose direction is perpendicular to the plane of 0 and F, show that M = RXF, where R is the vector from 0 to any point on the line of...