Of Motion: An Elementary Treatise |
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Page 7
... whence the same results are obtained . If we consider space of three dimensions , and the velocities along Ox , Oy , Oz be given v1 , V2 , V3 , = = V1 , 2 we have B C O D E A 21 OD2 = OE + ED2 , = OA2 + OB2 + 002 , OB cos DOx = = OA OD ...
... whence the same results are obtained . If we consider space of three dimensions , and the velocities along Ox , Oy , Oz be given v1 , V2 , V3 , = = V1 , 2 we have B C O D E A 21 OD2 = OE + ED2 , = OA2 + OB2 + 002 , OB cos DOx = = OA OD ...
Page 15
... whence x = r cos 0 , y = r sin 0 , ย dx dr de dt = cos 0 - r sin e dt dt ' dt dy = sin e d dr de + r cos 0 dt dt " and the velocity in direction of OP D = dx dt cos 0 + dy sin 0 = dr dt dt ' O I and the velocity in direction PT at right ...
... whence x = r cos 0 , y = r sin 0 , ย dx dr de dt = cos 0 - r sin e dt dt ' dt dy = sin e d dr de + r cos 0 dt dt " and the velocity in direction of OP D = dx dt cos 0 + dy sin 0 = dr dt dt ' O I and the velocity in direction PT at right ...
Page 16
... whence d2r dt2 does not express the acceleration in OP as d2x day and do those in the directions of x and y . A direct dt2 dt2 demonstration of these formula may be found in Sandeman's treatise Of the Motion of a Single Particle . It ...
... whence d2r dt2 does not express the acceleration in OP as d2x day and do those in the directions of x and y . A direct dt2 dt2 demonstration of these formula may be found in Sandeman's treatise Of the Motion of a Single Particle . It ...
Page 29
... Whence it is easily seen that the motion is oscillatory between two points whose distances from the origin area and a , and that the time of a complete oscillation is 4 . π - 2π = 2√λ 玩 position of the moving point . which is ...
... Whence it is easily seen that the motion is oscillatory between two points whose distances from the origin area and a , and that the time of a complete oscillation is 4 . π - 2π = 2√λ 玩 position of the moving point . which is ...
Page 41
... whence dow dt2 + w = 0 ; .. w = A cos ( 0 – B ) . 78. We have also 2 A2 ( du ) + u2 = 4a sin2 ( 0 − § ) + { } 3 + 4 cos ( 0 – B ) } " h2 λ 2λ == + A2 + h1 h2 A cos ( 0 - B ) ; 2 .. ( by Art . 64 ) ( velocity ) 2 = λ2 h2 + A2h2 + 2λA ...
... whence dow dt2 + w = 0 ; .. w = A cos ( 0 – B ) . 78. We have also 2 A2 ( du ) + u2 = 4a sin2 ( 0 − § ) + { } 3 + 4 cos ( 0 – B ) } " h2 λ 2λ == + A2 + h1 h2 A cos ( 0 - B ) ; 2 .. ( by Art . 64 ) ( velocity ) 2 = λ2 h2 + A2h2 + 2λA ...
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Common terms and phrases
accele acceleration produced axes axis balls center of force chord circle complete oscillation conic section constant acceleration cos² curve cycloid described determine the motion determined in Arts Differential Calculus direction of motion dt dt dt² earth's effect elastic ellipse equal equation fixed point focus force acting force of constraint force varying geometrical horizontal hyperbola impact impulse inclined plane inelastic initial direction initially at rest instant Ipswich School latus rectum Law of Motion length lowest point magnitude measure moving point NEWTON obtained Octavo orbit parabola parallelogram particle path perpendicular point of projection quantity of matter radius vector Second Edition Sermons shew sin² space passed straight line string supposed tangent tion Treatise Trinity College University of Cambridge v₁ versin vertex vis viva weight whence
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