Of Motion: An Elementary Treatise |
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Page 18
... preceding Articles to certain given quantities , and thus obtain sets of differential equations , the solution of which will determine the motion . As the expressions of the preceding Articles have all been derived from those in * These ...
... preceding Articles to certain given quantities , and thus obtain sets of differential equations , the solution of which will determine the motion . As the expressions of the preceding Articles have all been derived from those in * These ...
Page 30
... preceding Arti- cles ; where it must be borne in mind that the time is reckoned not from the actual beginning of the motion , but from the begin- ning of the hypothetical motion of the second point , i . e . that the time t in the preceding ...
... preceding Arti- cles ; where it must be borne in mind that the time is reckoned not from the actual beginning of the motion , but from the begin- ning of the hypothetical motion of the second point , i . e . that the time t in the preceding ...
Page 32
... preceding case , the moving point will come to rest at a distance a from the origin , after the lapse of a time . П √√ 3 It is now in the same cir- 27 cumstances as it initially was , but on the negative side of the origin , and ...
... preceding case , the moving point will come to rest at a distance a from the origin , after the lapse of a time . П √√ 3 It is now in the same cir- 27 cumstances as it initially was , but on the negative side of the origin , and ...
Page 43
... preceding Articles the conic section has been treated as if it were an ellipse : if e were > 1 , i . e . if it were an hyperbola , we should have a ( e2 - 1 ) = semi - latus rectum ; the only effect this has is to change the sign of a ...
... preceding Articles the conic section has been treated as if it were an ellipse : if e were > 1 , i . e . if it were an hyperbola , we should have a ( e2 - 1 ) = semi - latus rectum ; the only effect this has is to change the sign of a ...
Page 44
... preceding cases the direction of the accelera- tion had been away from the fixed point , the sign of a would have been changed , and the motion would be determined in an exactly similar manner : if we change the sign of λ in the two ...
... preceding cases the direction of the accelera- tion had been away from the fixed point , the sign of a would have been changed , and the motion would be determined in an exactly similar manner : if we change the sign of λ in the two ...
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Common terms and phrases
acceleration produced apse axes axis balls center of force chord circle co-ordinates complete oscillation conic section considered constant acceleration cos² curve cycloid described determine the motion Differential Calculus direction of motion ds dt dt² dx dy earth's elastic ellipse equal equation fixed point focus force acting geometrical horizontal hyperbola idea impact impulse inclined plane initial direction initial position initial velocity initially at rest instant under consideration latus rectum Law of Motion material bodies measure moving point negative NEWTON obtained Octavo orbit origin parabola parallelogram particle path perpendicular point be moving quantity of matter radius vector Second Edition Sermons shew sin² space passed Statics straight line string supposed tangent tion Treatise Trinity College units of space University of Cambridge v'cos v₁ velocity acquired vertex vertical vis viva weight whence ᏧᎾ
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