A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 81
... focus to the curve is equal to the latus rectum . 4. Determine the motion of a particle , initially at rest , under the action of a force to a fixed point varying inversely as the cube of the distance . 5. A hyperbola is placed in a ...
... focus to the curve is equal to the latus rectum . 4. Determine the motion of a particle , initially at rest , under the action of a force to a fixed point varying inversely as the cube of the distance . 5. A hyperbola is placed in a ...
Página 108
... focus and be reflected by the curve , it will fall to the lower vertex ; and shew that in an ellipse , whose eccentricity is 5 , this point will be the extremity of the minor axis . 11. A bullet is fired in the direction towards a ...
... focus and be reflected by the curve , it will fall to the lower vertex ; and shew that in an ellipse , whose eccentricity is 5 , this point will be the extremity of the minor axis . 11. A bullet is fired in the direction towards a ...
Página 109
... focus of the path is in the plane . If t and ť be the two times of flight corresponding to any range short of the greatest , and a be the inclination of the plane , prove that is independent of a . t2 + 2tt ' sin a + ť2 15. Two smooth ...
... focus of the path is in the plane . If t and ť be the two times of flight corresponding to any range short of the greatest , and a be the inclination of the plane , prove that is independent of a . t2 + 2tt ' sin a + ť2 15. Two smooth ...
Página 110
... focus of its path may be in the centre ; after reflection at the sphere shew that it will strike the horizontal plane at a distance from the point of projection equal to the diameter of the sphere , if the elasticity be perfect . 23 ...
... focus of its path may be in the centre ; after reflection at the sphere shew that it will strike the horizontal plane at a distance from the point of projection equal to the diameter of the sphere , if the elasticity be perfect . 23 ...
Página 122
... law of force to the focus under the action of which a conic section can be described . Taking as the equation of the conic d2u do2 = cu = 1 + e cos 0 , d2u d02 e cose , and + u = so that P = h2u2 C = h2 1 с 122 CENTRAL ORBIT .
... law of force to the focus under the action of which a conic section can be described . Taking as the equation of the conic d2u do2 = cu = 1 + e cos 0 , d2u d02 e cose , and + u = so that P = h2u2 C = h2 1 с 122 CENTRAL ORBIT .
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Términos y frases comunes
acting forces action angular momentum axes ball body centre of force centre of gravity chain circle circular component constant coordinates cos² curve cycloid described determine the motion diameter direction of motion disc distance ds ds Edition elastic string ellipse equal equations of motion equilibrium Fcap fixed point given h₁ heavy particle Hence hodograph horizontal plane hyperbola impulses inclination initial instant kinetic energy latus rectum mass moment of inertia momenta natural length normal obtain orbit parabola particle moves path perpendicular point moves position prove radius of curvature radius vector relative revolve ring rotation shew sin² smooth horizontal plane sphere straight line surface Taking tangent tension time-flux tube uniform angular velocity uniformly vertex vertical plane weight
Pasajes populares
Página 48 - 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.