A Collection of Problems in Illustration of the Principles of Theoretical MechanicsDeighton, Bell, 1876 - 667 páginas |
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Página 2
... origin will be given by the formula Jxy Sy da xy dx where the integrations are to be performed between limits de- pending upon the positions of the intercepting ordinates . The value of is sometimes more readily obtained by polar co ...
... origin will be given by the formula Jxy Sy da xy dx where the integrations are to be performed between limits de- pending upon the positions of the intercepting ordinates . The value of is sometimes more readily obtained by polar co ...
Página 3
William Walton. the origin , and the inclination of r to the axis of a . The nature of the limits in the double integrations will depend upon the form of the area in each particular case . Supposing the area to consist of several ...
William Walton. the origin , and the inclination of r to the axis of a . The nature of the limits in the double integrations will depend upon the form of the area in each particular case . Supposing the area to consist of several ...
Página 12
... origin of co - ordinates ; also , A being the vertex of the parabola , let ASx be the axis of x , and Sy at right angles to Sx the axis of y . Let SP = r , ‹ ASP = 0 , AS - m . Then for the position of the centre of gravity , if ASK ...
... origin of co - ordinates ; also , A being the vertex of the parabola , let ASx be the axis of x , and Sy at right angles to Sx the axis of y . Let SP = r , ‹ ASP = 0 , AS - m . Then for the position of the centre of gravity , if ASK ...
Página 15
... sin e do dr the pole being taken at the origin of x , and ✪ being the angle of inclination of the radius vector to the axis of x . ( 1 ) To find the centre of gravity of CENTRE OF GRAVITY . 15 III Solid of Revolution.
... sin e do dr the pole being taken at the origin of x , and ✪ being the angle of inclination of the radius vector to the axis of x . ( 1 ) To find the centre of gravity of CENTRE OF GRAVITY . 15 III Solid of Revolution.
Página 16
... origin its equation will be x2 + y2 = a2 .... ..... . ( 1 ) ; and , c being the distance of the centre of the plane face of the segment from the origin , but also x = [ * xy3 dx ↓ y2 dx a [ * xy3 dx = [ " ( a2 — x2 ) x da , from ( 1 ) ...
... origin its equation will be x2 + y2 = a2 .... ..... . ( 1 ) ; and , c being the distance of the centre of the plane face of the segment from the origin , but also x = [ * xy3 dx ↓ y2 dx a [ * xy3 dx = [ " ( a2 — x2 ) x da , from ( 1 ) ...
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Términos y frases comunes
absolute force acted angular velocity attraction axes axis beam body catenary centre of force centre of gravity circle co-ordinates coefficient of friction cos² curve cycloid cylinder denote density descends determine distance dt dt dt² dx dy dx² elastic ellipse equal equation Euler find the centre fixed point hence horizontal plane inclined plane inertia integrating James Bernoulli John Bernoulli lamina mass middle point moment of inertia motion natural length oscillation parabola perpendicular position of equilibrium pressure radius of gyration radius vector resolving forces rest right angles SECT sin² smooth sphere square straight line string supposing surface taking moments tangent tension triangle tube uniform rod varying inversely vertex vertical plane Vis Viva weight
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