Book:C.E. Weatherburn/Elementary Vector Analysis

Subject Matter

 * Vector Analysis

Contents



 * CHAPTER $\text {I}$.
 * 1. Scalar and vector quantities
 * 2. Length vectors
 * 3. Definitions of terms
 * 4. Addition and subtraction of vectors. Component and Resultant
 * 5. Multiplication by a number
 * 6. Resolution of a vector
 * 7. The unit vectors $\mathbf i$, $\mathbf j$, $\mathbf k$
 * 8. Division of a line in a given ratio
 * 9. Centroid, or centre of mean position
 * 10. Centroids of area and volume
 * 11. Centre of mass
 * 12. Relative position. Relative displacement. Uniform relative velocity
 * 13. Concurrent forces. Vector polygon. Lami's Theorem
 * 14. Soliution of examples


 * CHAPTER $\text {II}$.
 * 15. Introductory
 * 16. Vector equation of a straight line
 * 17. Bisector of the angle between two straight lines
 * 18. The Triangle
 * 19. The Tetrahedron
 * 20-1 Vector equation of a plane
 * 22. Linear relation independent of the origin
 * 23. Vector areas. Theorem for closed polyhedra


 * CHAPTER $\text {III}$.
 * Scalar and Vector Products.
 * 24. New use of terms product and multiplication
 * 25. Scalar product of two vectors
 * 26. The distributive law
 * 27. Vector product of two vectors
 * 28. The distributive law


 * Geometry of the Plane.
 * 29. Vector equation of a plane $\mathbf r \cdot \mathbf n = q$
 * 30. Distance of a point from a plane
 * 31. Plane through the intersection of two planes
 * 32. Distance of a point from a straight line


 * Geometry of the Sphere.
 * 33. Vector equation of a sphere
 * 34. Equation of the tangent plane at a point
 * 35. Polar plane of a point
 * 36. Diametral plane for parallel chords
 * 37-8. Radical plane of two spheres. System of spheres with a common radical plane


 * Applicaiton to Mechanics
 * 39. Work done by a force
 * 40. Vector moment or torque of a force about a point
 * 41. Angular velocity of a rigid body about a fixed axis


 * CHAPTER $\text {IV}$.
 * Triple and Quadruple Products
 * 42. Triple products
 * 43. Scalar triple product. Volume of parallelepiped. Coplanar vectors
 * 44. Vector triple product
 * 45. A scalar product of four vectors
 * 46. A vector product of four vectors. Relation between four vectors
 * 47. System of vectors reciprocal to $\mathbf {a, b, c}$


 * Further Geometry of the Plane and Straight Line.
 * 48. Planes satisfying various conditions
 * 49. Condition of intersection of two straight lines
 * 50. The common perpendicular to two non-intersecting straight lines
 * 51. Plücker's coordinates of a straight line
 * 52. Volume of a tetrahedron


 * ''Other Applications.
 * 53. Two formulae of Spherical Trigonometry
 * 54. Rankine's theorem for four concurrent forces


 * CHAPTER $\text {V}$.
 * Differentiation and Integration
 * 55. Derivative of a vector with respect to a scalar variable. Differentiation
 * 56. Derivatives of products
 * 57. Integration of vectors and products of vectors


 * Curvature and Torsion.
 * 58. Tangent to a curve at a given point
 * 59. Curvature. Principal normal. Plane of curvature or osculating plane
 * 60. Binormal. Torsion


 * Definite Integrals.
 * 61. Definite integral of a vector function
 * 62. Illustrations
 * 63. Line integral of a vector function
 * 64. Surface integral of a vector function


 * CHAPTER $\text {VI}$.
 * Kinematics.
 * 65. Velocity at an instant. Theorem of vector addition of velocities
 * 66. Acceleration at an instant. Theorem of vector addition of accelerations
 * 67. Tangential and normal residues of acceleration
 * 68. Radial and transverse residues of velocity and acceleration
 * 69. Areal velocity about a point
 * 70. Motion with constant acceleration


 * Dynamics.
 * 71. Momentum
 * 72. Newton's Second Law of Motion
 * 73. Impulse of a force. Impulsive forces
 * 74. Activity of a force
 * 75. The principle of energy
 * 76. Moment of momentum or angular momentum about a point. Principle of A.M.
 * 77. Central forces
 * 78. Central forces varying inversely as the square of the distance
 * 79. Planetary motion
 * 80. Central force varying directly as the distance
 * 81. Motion of a particle on a fixed curve


 * CHAPTER $\text {VII}$.
 * Dynamics of a System.
 * 82. Linear momentum of the system
 * 83. Acceleration of the centre of mass
 * 84. Angular momentum about a point
 * 85. Moving origin of moments. Centre of mass as origin
 * 86. Equations for impulsive forces


 * Kinematics of a Rigid Body
 * 87. Motion of a rigid body about a fixed point. Instantaneous axis of rotation
 * 88. General motion of a rigid body. Screw motion
 * 89. Simultaneous motions


 * Dynamics of a Rigid Body
 * 90. Angular momentum of a rigid body. Moments and products of inertia
 * 91. Principal axes of inertia
 * 92. Kinetic energy of a rigid body
 * 93. Principle of energy
 * 94. Moving axes or frame of reference
 * 95. Coriolis' Theorem
 * 96. Euler's dynamical equation


 * CHAPTER $\text {VIII}$.
 * 97. Conditions of equilibrium of a rigid body
 * 98. Equivalent systems of forces
 * 99. Parallel forces. Centre of gravity
 * 100. Couples. Composition of couples.
 * 101. Poinsot's reduction of a system of forces. Central axis. Equivalent wrench
 * 102. Null plane at a point
 * 103. Conjugate forces
 * 104. Principle of Virtual Work, or Virtual Velocities
 * 105. Equilibrium of a string under any forces
 * 106. Equilibrium of a wire under any forces