A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 63
... = 0 , leading to this gives x = Ae√ut + Be√ut , = √μ Aε √μt — √μ Bε - Nut , - and introducing the initial conditions we find that a = A + B , and 0 = AB , In the second case μ is of three dimensions in RECTILINEAR MOTION . 63.
... = 0 , leading to this gives x = Ae√ut + Be√ut , = √μ Aε √μt — √μ Bε - Nut , - and introducing the initial conditions we find that a = A + B , and 0 = AB , In the second case μ is of three dimensions in RECTILINEAR MOTION . 63.
Página 67
... ( x − 1 ft3 ) , - - or , if x − 1 ft2 = r , ï + f = − μr , or ï + μ ( r + 1 ) = 0 , the solution of which is r + μ = A cos √μt + B sin √μt . Introducing the initial conditions , we find A and B 5-2 RECTILINEAR MOTION . 67.
... ( x − 1 ft3 ) , - - or , if x − 1 ft2 = r , ï + f = − μr , or ï + μ ( r + 1 ) = 0 , the solution of which is r + μ = A cos √μt + B sin √μt . Introducing the initial conditions , we find A and B 5-2 RECTILINEAR MOTION . 67.
Página 68
William Henry Besant. Introducing the initial conditions , we find A and B , and thus determine x in terms of the time . 66. Motion of a heavy particle , suspended from a fixed point by an elastic string . If x be the length at the time ...
William Henry Besant. Introducing the initial conditions , we find A and B , and thus determine x in terms of the time . 66. Motion of a heavy particle , suspended from a fixed point by an elastic string . If x be the length at the time ...
Página 76
... conditions . If for instance x = a , initially , that is , if x be just greater than a , C = ga3 , ( x + a ) 3 v2 = 2o ( x − a ) 3 ( x + 2a ) . 2g 3 - Also , ( the tension at C ) × St momentum generated in the time St by the action of ...
... conditions . If for instance x = a , initially , that is , if x be just greater than a , C = ga3 , ( x + a ) 3 v2 = 2o ( x − a ) 3 ( x + 2a ) . 2g 3 - Also , ( the tension at C ) × St momentum generated in the time St by the action of ...
Página 80
... conditions consistent with equi- librium . The time in which this takes place is obtained by inte- grating the equation i -- 9 u2 ( 2uv — v2 ) , and the theoretical result is that an infinite time must elapse before the ball absolutely ...
... conditions consistent with equi- librium . The time in which this takes place is obtained by inte- grating the equation i -- 9 u2 ( 2uv — v2 ) , and the theoretical result is that an infinite time must elapse before the ball absolutely ...
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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.