A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 3
... integrating factor € 5 ( 2 ) , ye1m = √ F ( x ) e3 TM m dx + C. leading to For example , if dy У + dx sin x = tan , the factor is tan x , and therefore y tan x = 2 tan x − x + C. ( 2 ) day + n2y = 0 . dx2 Multiply by dy and integrate ...
... integrating factor € 5 ( 2 ) , ye1m = √ F ( x ) e3 TM m dx + C. leading to For example , if dy У + dx sin x = tan , the factor is tan x , and therefore y tan x = 2 tan x − x + C. ( 2 ) day + n2y = 0 . dx2 Multiply by dy and integrate ...
Página 62
... Integrating again , x = ft2 + ut + a , if a be the initial value of x . The equation may also be written in the form leading to dv = f , dx { v2 = { u2 + ƒx . 60. Motion of two weights connected by a fine string passing over a smooth ...
... Integrating again , x = ft2 + ut + a , if a be the initial value of x . The equation may also be written in the form leading to dv = f , dx { v2 = { u2 + ƒx . 60. Motion of two weights connected by a fine string passing over a smooth ...
Página 63
... integrate , we obtain x2 = μ ( α2 — x2 ) , - shewing as before that the velocity vanishes when x = ± α . If the force be repulsive the equation of motion is - x = μx , or ï— μx = 0 , leading to this gives x = Ae√ut + Be√ut , = √μ Aε ...
... integrate , we obtain x2 = μ ( α2 — x2 ) , - shewing as before that the velocity vanishes when x = ± α . If the force be repulsive the equation of motion is - x = μx , or ï— μx = 0 , leading to this gives x = Ae√ut + Be√ut , = √μ Aε ...
Página 70
... Integrating and taking u as the initial velocity , v2 + w2 u2 + w2 = € - 2gx w2 shewing that the particle rises to the height .. w2 2g log ( 1+ ) . 2gx Further , v3 = ( u2 + w3 ) € w2 - w3 . dt dx gx 6 202 2gx u2 + w2 - w2ε ' w2 which ...
... Integrating and taking u as the initial velocity , v2 + w2 u2 + w2 = € - 2gx w2 shewing that the particle rises to the height .. w2 2g log ( 1+ ) . 2gx Further , v3 = ( u2 + w3 ) € w2 - w3 . dt dx gx 6 202 2gx u2 + w2 - w2ε ' w2 which ...
Página 72
... Integrating this equation over the length of the chain we shall obtain an equation for determining a in terms of the time . Suppose for instance that the force is repulsive and varies as the distance from the point 0 , or that Integrating ...
... Integrating this equation over the length of the chain we shall obtain an equation for determining a in terms of the time . Suppose for instance that the force is repulsive and varies as the distance from the point 0 , or that Integrating ...
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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.