A Treatise on Dynamics of a Particle: With Numerous Examples |
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A Treatise on Dynamics of a Particle: With Numerous Examples (Classic Reprint) Peter Guthrie Tait No preview available - 2017 |
Common terms and phrases
acceleration apse apse line axes axis body brachistochrone center of attraction center of inertia central attraction central orbit circle circular co-ordinates component constant angular velocity cos² curvature curve cycloid d²x described determine the motion direction of motion distance ds ds ds² dt dt dt dt² dx dt dx dy dz ellipse equal equations of motion fixed point focus gravity Hence hodograph horizontal plane hyperbola impressed forces inclined initial instant integral inversely kinetic energy latus rectum law of attraction length logarithmic spiral mass osculating plane parabola parallel particle moves pendulum perpendicular point of projection position proportional prove radius vector resistance resolved rest resultant shew sin² smooth straight line suppose surface tangent tension tion tube v₁ velo vertex vertical
Popular passages
Page 49 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.
Page 49 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 53 - To every action there is always an equal and contrary reaction ; or the mutual actions of any two bodies are always equal and oppositely directed.
Page 74 - ... that line, and varying inversely as the square of the distance from that point ; find the time of a small oscillation about the position of equilibrium.
Page 99 - A particle is projected from a given point with a given velocity and is acted on by a given force to a fixed point.
Page 16 - Hence the moment of the resultant is equal to the sum of the moments of the two components.
Page 45 - In rectangular resolution the Component of a force in any direction, (sometimes called the Effective Component in that direction,) is therefore found by multiplying the magnitude of the force by the cosine of the angle between the directions of the force and the component. The remaining component in this case is perpendicular to the other. It is very generally convenient to resolve forces into components parallel to three lines at right angles to each other; each such resolution being effected by...
Page 54 - Si cestimetur agentis actio ex ejus vi et velocitate conjunctim ; et similiter resistentis reactio cestimetur conjunctim ex ejus partium singularum velocitatibus et viribus resistendi ab earum attritione, cohaesione, pondere, et acceleratione oriundis; erunt actio et reactio, in omni instrumentorum usu, sibi invicem semper cequales.
Page 36 - The highest point of the wheel of a carriage, rolling on a horizontal road, moves twice as fast as each of two points in the rim, whose distance from the ground is half the radius of the wheel.
Page 386 - L describe areas proportional to the times of describing them by radii drawn to another body T; and from the whole force which acts upon L, whether a single force or compounded of several forces, be...