Vectors and Rotors: With ApplicationsE. Arnold, 1903 - 204 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 28.
Σελίδα viii
... 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.
... 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 xii
... components of forces 148. Application to work done EXERCISES VIII . 115 115 115 116 CHAPTER IV . ROTORS . GEOMETRICAL THEORY . SECTION ( I ) . 149. Definition of a Rotor 150. Definition of a Rotor - Quantity 151. Specification of a ...
... components of forces 148. Application to work done EXERCISES VIII . 115 115 115 116 CHAPTER IV . ROTORS . GEOMETRICAL THEORY . SECTION ( I ) . 149. Definition of a Rotor 150. Definition of a Rotor - Quantity 151. Specification of a ...
Σελίδα 17
... components . the sum or resultant vector of the and we write σ = a + B + y + d . 32. The rule for the addition of vectors does not imply that the vectors are in a plane or , what amounts to the same thing , in parallel planes . If they ...
... components . the sum or resultant vector of the and we write σ = a + B + y + d . 32. The rule for the addition of vectors does not imply that the vectors are in a plane or , what amounts to the same thing , in parallel planes . If they ...
Σελίδα 22
... components aa and bß . No other triangle can be drawn having OB as one side and the other sides parallel to a and B. Since any multiple of y can be expressed in a similar way , we may say that in general between any three coplanar ...
... components aa and bß . No other triangle can be drawn having OB as one side and the other sides parallel to a and B. Since any multiple of y can be expressed in a similar way , we may say that in general between any three coplanar ...
Σελίδα 29
... say that any vector can be uniquely decomposed into two components having given directions ( coplanar with the vector ) . If the vector is the position vector of a point APPLICATIONS OF VECTORS TO GEOMETRY 29 Addition of two Vectors.
... say that any vector can be uniquely decomposed into two components having given directions ( coplanar with the vector ) . If the vector is the position vector of a point APPLICATIONS OF VECTORS TO GEOMETRY 29 Addition of two Vectors.
Περιεχόμενα
9 | |
10 | |
11 | |
12 | |
15 | |
17 | |
22 | |
25 | |
33 | |
40 | |
43 | |
46 | |
55 | |
56 | |
58 | |
59 | |
60 | |
63 | |
64 | |
65 | |
66 | |
68 | |
69 | |
70 | |
72 | |
73 | |
74 | |
76 | |
77 | |
78 | |
79 | |
80 | |
81 | |
95 | |
96 | |
97 | |
98 | |
99 | |
100 | |
101 | |
102 | |
103 | |
104 | |
105 | |
106 | |
107 | |
108 | |
110 | |
114 | |
116 | |
118 | |
121 | |
127 | |
150 | |
155 | |
156 | |
161 | |
164 | |
170 | |
171 | |
178 | |
183 | |
184 | |
195 | |
201 | |
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...