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A Treatise on the Dynamics of a Particle, by P.G. Tait and W.J. Steele
Peter Guthrie Tait,William John Steele
No preview available - 2016
acceleration acted action angle angular velocity apse apsidal apsidal distances axes axis body center of force central force central orbit chord circle co-ordinates conic section constant cos˛ curvature curve cycloid d˛x described determine the motion direction of motion direction of projection directrix ds ds ds dt dt ds dt dt dt dt dx dt dy dt˛ dx dt dx dy dy dt dy dz ellipse equal equation of motion evidently fixed point focus given point given velocity gravity Hence hodograph hyperbola inclined plane initial instant integral kinetic latus rectum law of force mass orbit oscillation osculating plane parabola parallel particle is projected particle moves path perpendicular point of projection position radius vector relative motion resolved resultant shew sin˛ straight line string surface tangent velo vertex
Page ii - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.
Page 40 - 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 86 - ... g sin 0 parallel to the line of greatest slope on the plane, and therefore the trajectory will still be a parabola, whose dimensions will depend upon 0. Ex. A particle is projected from a given point with a given velocity, and moves on an inclined plane/ find the locus of the directrices of its path for different inclinations of the plane. It will be easily seen that when a particle moves on an inclined plane, the velocity at any point is equal to that which would have been acquired by sliding...
Page 44 - 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 ii - FROST.— The First Three Sections of Newton's Principia. With Notes and Problems in illustration of the subject. By PERCIVAL FROST, MA late Fellow of St.
Page 14 - Hence the moment of the resultant is equal to the sum of the moments of the two components.
Page 70 - The straight line down which a particle will slide in the shortest time from a given point to a given circle in the same vertical plane, is the line joining the point to the upper or lower extremity of the vertical diameter, according as the point is within or without the circle.
Page 302 - B, 0, &c. for which e is given, are placed in a line ; A is projected with given velocity so as to impinge on B, B then impinges on C, and so on ; find the masses of the balls B, C, &c. in order that each of the balls A, B, C, &c.
Page 44 - From this it follows that the sum of the quantities of motion, parallel to any fixed direction, of the particles of any system influencing one another in any possible way, remains unchanged by their mutual action ; also that the sum of the moments of momentum of all the particles...