Elementary Vector Analysis: With Application to Geometry and Physics |
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Common terms and phrases
acceleration algebra angle angular momentum angular velocity areal velocity associated numbers central force centre of force centroid common perpendicular constant coordinates coplanar curve d³r denoted displacement dr dt dt dt ellipse equation of motion equilibrium equivalent external forces fixed point force F forces acting formula Hence hodograph inertia instantaneous integration interval kinetic energy length limiting value line joining line of action line of intersection mass mid points module moments of inertia orbit origin parallel perpendicular plane containing plane of curvature polar plane position vector relative principal normal Prove Quaternions radical plane radius rate of increase rectangular represented respectively resultant rigid body rotation S₁ S₂ scalar product scalar triple product Show speed sphere square straight line surface t₁ tangent tetrahedron theorem torque triangle unit vector v₁ variable vector area vector equation vector quantity vector sum δι
Popular passages
Page 32 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 59 - Find the locus of a point which moves so that the difference of the squares of its distances from two fixed points is constant.
Page xxii - Even Prof. Willard Gibbs must be ranked as one of the retarders of quaternion progress, in virtue of his pamphlet on Vector} Analysis; a sort of hermaphrodite monster, compounded of the notations of Hamilton and of Grassmann.
Page 58 - ... is equal to four times the sum of the squares on the sides of the triangle.
Page 59 - A point moves so that its distances from two fixed points are in a constant ratio k.
Page 16 - If three forces acting on a particle keep it in equilibrium, each is proportional to the sine of the angle between the other two.
Page 33 - ... a straight line is drawn parallel to the base of a triangle, the corresponding segments on the two sides are in a constant ratio.
Page 121 - ... a single particle of mass equal to the total mass of the system, and placed at the centre of inertia.
Page 118 - ... on arriving at the extremity of the minor axis, the force has its law changed, so that it varies as the distance, the magnitude at that point remaining...
Page xxii - was, I think, defined by an American schoolgirl to be "an ancient religious ceremony." This was, however, a complete mistake. The ancients — unlike Prof. Tait — knew not, and did not worship Quaternions. The quaternion and its laws were discovered by that extraordinary genius Sir W. Hamilton.