A Collection of Problems in Illustration of the Principles of Theoretical Mechanics |
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Page v
... Curve CHAPTER I. . VI . Curve of Double Curvature VII . Surface of Revolution VIII . Any Surface • IX . Heterogeneous Bodies X. Centre of Parallel Forces XI . The Properties of Pappus PAGE 1 2 9 15 19 25 27 28 30 35 37 39 Equilibrium of ...
... Curve CHAPTER I. . VI . Curve of Double Curvature VII . Surface of Revolution VIII . Any Surface • IX . Heterogeneous Bodies X. Centre of Parallel Forces XI . The Properties of Pappus PAGE 1 2 9 15 19 25 27 28 30 35 37 39 Equilibrium of ...
Page vii
... Curves . 291 Inverse Problems on the Motion of a Particle along immove- able Plane Curves 299 IV . Inverse Problems on ... Curve revolving about an Axis within its own Plane A Material Line revolving about an Axis at Right Angles to its ...
... Curves . 291 Inverse Problems on the Motion of a Particle along immove- able Plane Curves 299 IV . Inverse Problems on ... Curve revolving about an Axis within its own Plane A Material Line revolving about an Axis at Right Angles to its ...
Page 3
... curve will be y ' = 4mx , m being the distance of the point P from the focus . Hence , if PE = a , xy dx ៤ ៖ fryde fade 4 Syde fade dx 0 a xdx 3-10 . za . dx fa * Archimedes , ' Emédov iσopponiкwv , Lib . II . Prop . 8 ; Guldin , Cen ...
... curve will be y ' = 4mx , m being the distance of the point P from the focus . Hence , if PE = a , xy dx ៤ ៖ fryde fade 4 Syde fade dx 0 a xdx 3-10 . za . dx fa * Archimedes , ' Emédov iσopponiкwv , Lib . II . Prop . 8 ; Guldin , Cen ...
Page 8
... curve and a double ordinate . The equation to the curve being ay = x , we shall have x = x . ( 6 ) To find the centre of gravity of the whole area of the curve of which the equation is y ' = f1 a = x . b2 x = a . x ( 7 ) To find the ...
... curve and a double ordinate . The equation to the curve being ay = x , we shall have x = x . ( 6 ) To find the centre of gravity of the whole area of the curve of which the equation is y ' = f1 a = x . b2 x = a . x ( 7 ) To find the ...
Page 9
... curve . It frequently happens that the method of polar co - ordinates is more convenient for the determination of x and ỹ than that by rectangular co - ordinates : the formula will be Ꮎ fr con de dr Sfr de dr " y = sine de dr Sfr de dr ...
... curve . It frequently happens that the method of polar co - ordinates is more convenient for the determination of x and ỹ than that by rectangular co - ordinates : the formula will be Ꮎ fr con de dr Sfr de dr " y = sine de dr Sfr de dr ...
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Common terms and phrases
absolute force acted angular velocity attraction axes axis body catenary centre of force centre of gravity circle co-ordinates coefficient of friction collision cos² curve cylinder d²x denote density determine direction distance dx dy dx² elastic ellipse equal equation Euler find the centre find the position fixed point formula given velocity hence horizontal plane inclined plane integrating James Bernoulli John Bernoulli latus rectum middle point motion oscillation parabola particle perpendicular position of equilibrium pressure problem projection radius of gyration rest right angles SECT shews sin² smooth sphere square straight line string supposing surface taking moments tan² tangent tension triangle tube unit of mass varying inversely vertical plane virtual velocities Vis Viva weight zero
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