Vectors and Rotors: With ApplicationsE. Arnold, 1903 - 204 σελίδες |
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Σελίδα viii
... TO GEOMETRY . SECTION ( II ) . EXERCISES I. 45. Geometrical examples • 46. Vectors and Coordinates 47. Equal Vectors equal components . 2222 24 27 29 31 § 48. One Vector equation equivalent to two Scalar equations viii CONTENTS.
... TO GEOMETRY . SECTION ( II ) . EXERCISES I. 45. Geometrical examples • 46. Vectors and Coordinates 47. Equal Vectors equal components . 2222 24 27 29 31 § 48. One Vector equation equivalent to two Scalar equations viii CONTENTS.
Σελίδα ix
With Applications Olaus Henrici, George Charles Turner. § 48. One Vector equation equivalent to two Scalar equations 49. Distance between two points PAGE 31 32 EXERCISES II . 32 • 50 . Vectors in Space 33 51. Any vector expressed in ...
With Applications Olaus Henrici, George Charles Turner. § 48. One Vector equation equivalent to two Scalar equations 49. Distance between two points PAGE 31 32 EXERCISES II . 32 • 50 . Vectors in Space 33 51. Any vector expressed in ...
Σελίδα xii
... Equivalent systems of Rotors , ( 2 ) Resultant Rotor , 119 119 • • 119 . 120 120 121 • 121 122 ( 3 ) Equilibrium of Rotors 122 158. If two rotors have equal momental areas for all poles , the rotors are equal . If a system of Rotors has ...
... Equivalent systems of Rotors , ( 2 ) Resultant Rotor , 119 119 • • 119 . 120 120 121 • 121 122 ( 3 ) Equilibrium of Rotors 122 158. If two rotors have equal momental areas for all poles , the rotors are equal . If a system of Rotors has ...
Σελίδα xiii
... equivalent to a single rotor and a couple 176. The Equilibrium of Rotors , EM = 0 for three non - col- linear points 177. Equilibrium of ( a ) two rotors , ( b ) three rotors 178. Resultant and Equilibrant SECTION ( II ) . FORCES . 179 ...
... equivalent to a single rotor and a couple 176. The Equilibrium of Rotors , EM = 0 for three non - col- linear points 177. Equilibrium of ( a ) two rotors , ( b ) three rotors 178. Resultant and Equilibrant SECTION ( II ) . FORCES . 179 ...
Σελίδα 9
... equivalent to the one step AC , hence we write AB + BC AC , = and this defines the addition of steps in a line . A A Fig . 6 . It will be seen that the formula is true whatever the position of the points B in the line may be , the two ...
... equivalent to the one step AC , hence we write AB + BC AC , = and this defines the addition of steps in a line . A A Fig . 6 . It will be seen that the formula is true whatever the position of the points B in the line may be , the two ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ ABCD Algebra angle axis B₁ bars base beam bending bending moment bisect C₁ called centre collinear Commutative Law components compression coordinates coplanar couple definite denote determined diagonals direction and sense distance divide draw drawn equal equation equilibrium figure find the mass-centre forces acting frame friction given points given rotor Hence the mass-centre horizontal length line joining line parallel link-polygon load m₁ magnitude mass mid-point momental area move multiplying negative number of vectors origin orts parallel rotors parallelogram parallelopiped perpendicular plane pole polygon position vector projection quadrilateral reaction rectangle represent resultant rigid body scalar product shearing force shew shewn sides straight line stress diagram string suppose symmetry system of rotors tension tetrahedron theorem three vectors triangle vanishes vector product vector-polygon vertex vertices weight
Δημοφιλή αποσπάσματα
Σελίδα 21 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 29 - If the exterior angle of a triangle be bisected by a straight line which also cuts the base produced, the segments between the bisecting line and the extremities of the base have the same ratio which the other sides of the triangle have to one another...
Σελίδα 8 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
Σελίδα 112 - ... is equal to the rectangle contained by the segments of the other.
Σελίδα 56 - ... are 8 in. Find the surface and volume of the greatest possible cylinder, of the same axis, that can be cut from the prism. Ex. 1634. The base of a right pyramid is a regular hexagon whose sides are 20 in., and the lateral faces are inclined to the base at an angle of 60°. Find the volume. Ex. 1635. Lines joining the mid.points of opposite edges of a tetrahedron meet in a point and bisect each other. Ex. 1636. The altitude of a cone of revolution is 27 in., and its curved surface is 7 times the...
Σελίδα 29 - The parallelograms about the diameter of any parallelogram are similar to the whole, and to one another. Let...
Σελίδα 116 - Show that the work done by a force in producing a given displacement may be measured (1) by the product of the displacement and the component of the force in the direction of the displacement...
Σελίδα 181 - A, the algebraic sum of the moments of all the forces to the left of the section is zero, since there are no forces to the left.
Σελίδα 3 - In vector geometry, a vector quantity is represented diagrammatically by a line called a vector. The length of the line represents, to scale, the magnitude of the quantity, and its direction represents the direction in which the quantity acts.
Σελίδα 29 - L' and L" cut at right angles. (8) Prove that the three bisectors of the angles of a triangle meet in a point. (9) Show that the equation of a straight line in polar co-ordinates is of the form r = p cosec (в — ф). What is the meaning of "p...