Of Motion: An Elementary Treatise |
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Page viii
... focus 44. Position of the vertex • 45. Magnitude of the latus rectum 21 ib . ib . 23 ib . 24 • 47. Velocity at any point ib . 48. Investigation of the above by means of the differential calculus . 25 CHAPTER IV . OF THE MOTION OF A ...
... focus 44. Position of the vertex • 45. Magnitude of the latus rectum 21 ib . ib . 23 ib . 24 • 47. Velocity at any point ib . 48. Investigation of the above by means of the differential calculus . 25 CHAPTER IV . OF THE MOTION OF A ...
Page 23
... focus 1 == · 22'2 ว = 12 4 α 2α • 43. The position of the focus S is determined as follows : SAB = 90 ° - SAY = 90 ° -2 . TAY = 90 ° -2 ( 90 ° - 1 ) — 21 — 90 ° ; = therefore if CSB be the axis , 12 = AB SA cos SAB = - = sin 20 2α 12 ...
... focus 1 == · 22'2 ว = 12 4 α 2α • 43. The position of the focus S is determined as follows : SAB = 90 ° - SAY = 90 ° -2 . TAY = 90 ° -2 ( 90 ° - 1 ) — 21 — 90 ° ; = therefore if CSB be the axis , 12 = AB SA cos SAB = - = sin 20 2α 12 ...
Page 37
... focus were the origin , the extremities of the major axis only are apses . + This case of motion may be easily solved in the following manner . We have the acceleration in a = -λr cos 0 = −λx , and that in y = — \ r sin 0 = − λy ...
... focus were the origin , the extremities of the major axis only are apses . + This case of motion may be easily solved in the following manner . We have the acceleration in a = -λr cos 0 = −λx , and that in y = — \ r sin 0 = − λy ...
Page 40
... fixed point . ... u = 1+ - λ h2 Then a = = λu2 ; α λ d2 u + u = h2 u2 = h2 ; d02 d de 2 2 = -1 -1 2 ( + d de +1 1 ) . ( 0 ) , + A cos ( 0 - B ) , MOTION IN A CONIC SECTION ABOUT THE FOCUS . 41 40 DETERMINATION OF THE PERIOD .
... fixed point . ... u = 1+ - λ h2 Then a = = λu2 ; α λ d2 u + u = h2 u2 = h2 ; d02 d de 2 2 = -1 -1 2 ( + d de +1 1 ) . ( 0 ) , + A cos ( 0 - B ) , MOTION IN A CONIC SECTION ABOUT THE FOCUS . 41 40 DETERMINATION OF THE PERIOD .
Page 41
An Elementary Treatise John Robert Lunn. MOTION IN A CONIC SECTION ABOUT THE FOCUS . 41 h2 or u = 1 + λ Ah2 cos ( 0 – B ) . λ This is the equation to a conic section whose focus is at the pole , 2h2 the angle vector of the apse being B ...
An Elementary Treatise John Robert Lunn. MOTION IN A CONIC SECTION ABOUT THE FOCUS . 41 h2 or u = 1 + λ Ah2 cos ( 0 – B ) . λ This is the equation to a conic section whose focus is at the pole , 2h2 the angle vector of the apse being B ...
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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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