A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 18
... Hence , observing that T Ꮎ ( da ) 2 + ( dy ) ds ds & P = 1 , dx d2x dy d3y and therefore + = 0 , ds ds2 ds ds2 it follows that Ꮖ tangential acceleration = s . Also , normal acceleration inwards = dx y ds - dy ds ( dx dy dy d2x ) ...
... Hence , observing that T Ꮎ ( da ) 2 + ( dy ) ds ds & P = 1 , dx d2x dy d3y and therefore + = 0 , ds ds2 ds ds2 it follows that Ꮖ tangential acceleration = s . Also , normal acceleration inwards = dx y ds - dy ds ( dx dy dy d2x ) ...
Página 21
... Hence , the velocity of P being compounded of its velocity with regard to N , and of the velocity of N , the components parallel to x and y are respectively • — xả cot - - yo cosec w , cot . ỷ + xẻ cosec co + y In exactly the same ...
... Hence , the velocity of P being compounded of its velocity with regard to N , and of the velocity of N , the components parallel to x and y are respectively • — xả cot - - yo cosec w , cot . ỷ + xẻ cosec co + y In exactly the same ...
Página 23
... Hence μOQ is the actual velocity of Q. Further if QE , QF represent the component velocities in direction and magnitude , the resulting velocity of Qis represented by QG the diagonal of the parallelogram , and the angle OQG = PQG - PQO ...
... Hence μOQ is the actual velocity of Q. Further if QE , QF represent the component velocities in direction and magnitude , the resulting velocity of Qis represented by QG the diagonal of the parallelogram , and the angle OQG = PQG - PQO ...
Página 24
... = a0 - a sin 0 , and y = a - a cos 0 , from which = a0 — a ( cos 0 . Ö — sin 0 . Ò3 ) , ÿ - - = a ( sin 0 . Ö + cos 0. Ô2 ) , and , putting 0 = 0 , ï = 0 , and ÿ = aỞ2 . Q We hence infer that if p be the radius of 24 PHORONOMY .
... = a0 - a sin 0 , and y = a - a cos 0 , from which = a0 — a ( cos 0 . Ö — sin 0 . Ò3 ) , ÿ - - = a ( sin 0 . Ö + cos 0. Ô2 ) , and , putting 0 = 0 , ï = 0 , and ÿ = aỞ2 . Q We hence infer that if p be the radius of 24 PHORONOMY .
Página 25
... Hence , if St be the time , the accelerations are the limits of wPQ and , as PQ = pd0 , the first of sin 80 δι and wPQ cos 60 St " these ultimately vanishes , and the second = w2p . ( 4 ) A circle of radius b rolls on a circle of radius ...
... Hence , if St be the time , the accelerations are the limits of wPQ and , as PQ = pd0 , the first of sin 80 δι and wPQ cos 60 St " these ultimately vanishes , and the second = w2p . ( 4 ) A circle of radius b rolls on a circle of radius ...
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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.