## Of Motion; an elementary treatise1859 |

### From inside the book

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Page 37

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**ellipse**whose center is at the pole , and the angle vector of its apse * is B. If the acceleration were in the opposite direction , the sign of λ would be changed , and the equation ( b ) would represent an hyperbola whose center is at ... Page 38

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**ellipse**. d2x therefore dt2 + λ = 0 , and + λy = 0 . day dt2 ... as in Art . 51 , x = A cos ( √ . t − ẞ ) , and y ...**ellipse**or an hyperbola we have 2C ( -20 ) -4 4 . 1 1 A2 4 · ́A2Ã ' ? ( 1 — C2 ) , AA ' which is negative , C ... Page 40

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**ellipse**, we have h 7-2 ( period ) = area of**ellipse**( Art . 62 ) ; .. period 2π ab 2π √λa2b2 √ which is independent of the form of the**ellipse**, and is therefore the same for all**ellipses**described under accelerations subject to the ... Page 41

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**ellipse**, parabola , or hyperbola , according as Ah2 λ is < = or > 1 . 77. This might have been obtained , as in Art . 52 , by putting λ - h2 = w , whence d'w dt + w = 0 ; .. w = A cos ( 0 – B ) . 78. We have also ( du \ 2 do + u2 = 42 ... Page 43

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**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 : then we shall have 2λ = + If e were = 1 , i . e . if the curve were a ...### Other editions - View all

### Common terms and phrases

acceleration produced apse axes axis balls called center of force circle complete oscillation conic section considered constant acceleration cos² curve cycloid d²r d²x described determine the motion Differential Calculus direction of motion distance ds dt dt dt dt dt² dx dy elastic ellipse equal equation experiments fixed point force acting geometrical h²C horizontal hyperbola idea impact impulse inclined plane initial direction initial position initial velocity initially at rest latus rectum Law of Motion mass material bodies measure moving point NEWTON obtained orbit parabola parallelogram particle path perpendicular point be moving quantity of matter radius vector Second Edition semi-latus rectum 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