A Treatise on Dynamics |
Other editions - View all
Common terms and phrases
accelerating-force action angle angular velocity apply apse attraction axis body moving C₁ called center of gravity co-ordinates considered cos² curve D'Alembert's principle d²x d2x dt2 da)² definite integral described determine the motion distance dt dt dt dt dx dt dy dt² dv dt dx dt dx dx dx dy dy dt dy dx dy dy effective force ellipse equal equations of motion equilibrium expression fixed point force acting forces which act function geometrical given h₁ Hence impressed forces impulse increase instant integration internal forces interval m₁ magnitude mass method negative obtained orbit origin osculating plane particle perfect differential plane position principle problem quantities rest rigid body shews sin² space suppose t₁ takes place v₁ vis viva viva zero δι Ση
Popular passages
Page 32 - NEWTON was able to formulate his great law of universal gravitation in these comprehensive words: "Every particle of matter in the universe attracts every other particle with a force directly as the masses of the two particles, and, inversely as the square of the distance which separates them." To show the nature of the attractive forces among these various particles, let us represent by m and m' the masses of two attracting bodies. We may conceive the body m to be composed of m particles, and the...
Page 52 - A body is projected with a velocity v in a direction making an angle a with the horizon...
Page 21 - MASS AND WEIGHT.— The mass of a body is the quantity of matter in it ; the weight of a body is due to the force of gravity acting upon this matter.
Page 32 - GRAVITATION.* — Every particle of matter in the universe attracts every other particle of matter with a force directly proportional to its mass, and decreasing as the square of the distance Fig.
Page 15 - If two forces acting at a point be represented in magnitude and direction by the sides of a parallelogram, the resultant of these two forces will be represented in magnitude and direction by the diagonal of the parallelogram passing through this point.
Page 91 - Remembering that the resistance of the air varies as the square of the velocity, it might easily be shown that the strength should be at least eight times, instead of twice, as great. Passing to the question of power. The soaring of birds is a most important fact, of which no one who has taken the trouble to make observations has any doubt. Though it was lately the subject of a...
Page 150 - That is, if the resultant of all the external forces applied to a body is zero, the center of gravity will move in a straight line with uniform velocity. This is a generalization of Newton's First Law of Motion. REMARK. — It will be noticed that the above reasoning applies also to a non-rigid system of particles if the internal forces are in equilibrium among themselves. For example, so far as...
Page 172 - OA of the smaller circle to represent the direction of the incident ray, and let NAB be the direction of the normal to the surface at the point of incidence, so that 0 AN is the angle of incidence.
Page 136 - The motion about the center of gravity is the same as if the center of gravity were fixed in space and the actual forces were unchanged in magnitude, direction, and point of application.
Page 53 - ... substituted in (a), gives y*=4hx, (62) the equation of a parabola referred to the oblique axes AX, AY ; and, since 4A is the parameter to the diameter through A, h is the distance from A, the point of projection to the focus F, or to the directrix. COR. The velocity of the body at any point of its path is that which the body would acquire in falling vertically from the directrix to that point. For if the body were projected from any point of its path in the direction, and with the velocity it...