Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 1
... axes originating in the centre and parallel to those to which x , y refer , x = a + x ' , y = b + y ' . .. Σ ( mxy ) = Σ ( m ) . ab + aΣ ( my ' ) + bΣ ( mx ' ) + Σ ( mx'y ' ) . Now = or Σ ( mx ' ) = Σ ( my ' ) = of ' by properties of ...
... axes originating in the centre and parallel to those to which x , y refer , x = a + x ' , y = b + y ' . .. Σ ( mxy ) = Σ ( m ) . ab + aΣ ( my ' ) + bΣ ( mx ' ) + Σ ( mx'y ' ) . Now = or Σ ( mx ' ) = Σ ( my ' ) = of ' by properties of ...
Page 2
... axes of co - ordinates , is da.dy , and this may also represent the mass of a corresponding element of the lamina if the mass of an unit of area of the lamina be unity ; .. Σ ( mxy ) = fzfy xy . Now first the summation of the values of ...
... axes of co - ordinates , is da.dy , and this may also represent the mass of a corresponding element of the lamina if the mass of an unit of area of the lamina be unity ; .. Σ ( mxy ) = fzfy xy . Now first the summation of the values of ...
Page 3
... axes . Let x , y be the co - ordinates of the point x , y , when re- ferred to other rectangular axes in the plane of xy so that x ' is in the axis of the cone ; :: . x = ' cos a - y ' sin al y = x ' sin a + y ' cos a The facility of ...
... axes . Let x , y be the co - ordinates of the point x , y , when re- ferred to other rectangular axes in the plane of xy so that x ' is in the axis of the cone ; :: . x = ' cos a - y ' sin al y = x ' sin a + y ' cos a The facility of ...
Page 5
... axes of one stratum . geneous spheroid bounded by this surface will have about its axis of figure the moment of inertia paß , p being its density , or pa3√1 – e2 . - Now if this expression be differentiated with regard to a OF A RIGID ...
... axes of one stratum . geneous spheroid bounded by this surface will have about its axis of figure the moment of inertia paß , p being its density , or pa3√1 – e2 . - Now if this expression be differentiated with regard to a OF A RIGID ...
Page 7
... axes in question . 7. Let x ' , y ' , x ' be co - ordinates of a particle m referred to co - ordinate axes through a point in the axis of ≈ at distance y from the origin of the co - ordinates x , y , z , the axes of and being the same ...
... axes in question . 7. Let x ' , y ' , x ' be co - ordinates of a particle m referred to co - ordinate axes through a point in the axis of ≈ at distance y from the origin of the co - ordinates x , y , z , the axes of and being the same ...
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2g h accelerating force Algebra angle angular velocity ball blow c² a² CA² Calculus Cambridge centre of gravity co-ordinate axes cone Conic Sections cos² cube cylinder diameter Differential Differential Calculus direction cosines disc distance dt dt dt dy dx dt dy dt effective force Examples Geometry Hence horizontal action horizontal and vertical HYMERS DR impulse inertia instantaneous axis invariable plane length Let C fig Ma² mass Mk² moment of inertia moves Mr² oscillation P₁ P₂ parallel particle perpendicular plates point of contact position pressure principal axes principle R₁ radius reaction revolves rotation sin² sphere tan² Third Edition Treatise velocities of translation vis viva w₁ w₂ wheel WHEWELL DR аф ᏧᎾ
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