An Elementary Treatise on the Dynamics of a System of Rigid Bodies |
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Common terms and phrases
angle angular velocity axis of rotation centre of gravity co-ordinates cone constant cos² couple D'Alembert's principle determine diameter differential coefficients direction displacement distance dt dt effective forces ellipse equal equations of motion fixed in space fixed point friction function geometrical equations given Hence horizontal plane impact impressed forces impulsive initial values instantaneous axis integral invariable line length mass moment of inertia momental ellipsoid moments of inertia momentum moving axes normal oscillation parallel particle pendulum perfectly rough perpendicular point of contact polhode principal axes principal moments product of inertia prove quadric radius of gyration ratio resolved resultant round sin² sliding small oscillations sphere straight line string Substituting suppose taking moments tangent plane theorem tion triangle vertical vis viva viva w₁ w₂ zero аф
Popular passages
Page 69 - May one thousand eight hundred and twenty-five, the Straight Line or Distance between the Centres of the Two Points in the Gold Studs in the Straight Brass Rod, now in the Custody of the Clerk of the House of Commons, whereon the Words and Figures
Page 132 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.
Page 204 - When it strikes the ground, supposed perfectly rough and inelastic, the centre is moving with velocity V in a direction making an angle a with the horizon, prove that the direction of the motion of the ball after impact will make with the plane of projection an angle tan~1 •= -= - , where a is the radius of the ball.
Page 439 - ... angular velocity about any axis of the earth perpendicular to the axis of figure. Let us now consider how this motion is disturbed by the action of the sun. The sun attracts the parts of the earth nearer to it with a slightly greater force than it attracts those more remote. Hence when the sun is either north or south of the equator its attraction will produce a couple tending to turn the earth about that axis in the plane of the equator which is perpendicular to the line joining the centre of...
Page 32 - Take the straight line as axis of z, and any point 0 in it as origin. Let C be the point at which it is a principal axis, and let Cx', Cy' be the other two principal axes. Let C0 = h, 0 = angle between Cx and Ox. Then x
Page 179 - A particle is projected with a velocity V in a direction making an angle a with the horizontal plane, and...
Page 69 - Pendulum vibrating Seconds of Mean Time in the Latitude of London in a Vacuum at the Level of the Sea...
Page 58 - Slephano del Bosco, were observed to have undergone a movement of a singular kind. The shock, which agitated the building, is described as having been horizontal and vorticose. The pedestal of each obelisk remained in its original place, but the separate stones above were turned partially round, and removed sometimes nine inches from their position without falling.
Page 137 - Q is only moved by the translation PN, ie Q is moved along QS. 226. It follows from this reasoning that any displacement of a body can be represented by a rotation about some straight line and a translation parallel to that straight line. This mode of constructing the displacement is called a screw. The straight line is sometimes called the central axis and sometimes the axis of the screw. The ratio of the translation to the angle of rotation is called the pitch of the screw.
Page 63 - Let jl/fc* be the moment of inertia of the iron jar and rod about the axis of suspension, c the distance of their common centre of gravity from that axis. Let...